ScalarEvolution.cpp revision 992efb03785f2a368fbb63b09373be1d6a96ce5a
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file is distributed under the University of Illinois Open Source 6// License. See LICENSE.TXT for details. 7// 8//===----------------------------------------------------------------------===// 9// 10// This file contains the implementation of the scalar evolution analysis 11// engine, which is used primarily to analyze expressions involving induction 12// variables in loops. 13// 14// There are several aspects to this library. First is the representation of 15// scalar expressions, which are represented as subclasses of the SCEV class. 16// These classes are used to represent certain types of subexpressions that we 17// can handle. We only create one SCEV of a particular shape, so 18// pointer-comparisons for equality are legal. 19// 20// One important aspect of the SCEV objects is that they are never cyclic, even 21// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 22// the PHI node is one of the idioms that we can represent (e.g., a polynomial 23// recurrence) then we represent it directly as a recurrence node, otherwise we 24// represent it as a SCEVUnknown node. 25// 26// In addition to being able to represent expressions of various types, we also 27// have folders that are used to build the *canonical* representation for a 28// particular expression. These folders are capable of using a variety of 29// rewrite rules to simplify the expressions. 30// 31// Once the folders are defined, we can implement the more interesting 32// higher-level code, such as the code that recognizes PHI nodes of various 33// types, computes the execution count of a loop, etc. 34// 35// TODO: We should use these routines and value representations to implement 36// dependence analysis! 37// 38//===----------------------------------------------------------------------===// 39// 40// There are several good references for the techniques used in this analysis. 41// 42// Chains of recurrences -- a method to expedite the evaluation 43// of closed-form functions 44// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 45// 46// On computational properties of chains of recurrences 47// Eugene V. Zima 48// 49// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 50// Robert A. van Engelen 51// 52// Efficient Symbolic Analysis for Optimizing Compilers 53// Robert A. van Engelen 54// 55// Using the chains of recurrences algebra for data dependence testing and 56// induction variable substitution 57// MS Thesis, Johnie Birch 58// 59//===----------------------------------------------------------------------===// 60 61#define DEBUG_TYPE "scalar-evolution" 62#include "llvm/Analysis/ScalarEvolutionExpressions.h" 63#include "llvm/Constants.h" 64#include "llvm/DerivedTypes.h" 65#include "llvm/GlobalVariable.h" 66#include "llvm/GlobalAlias.h" 67#include "llvm/Instructions.h" 68#include "llvm/LLVMContext.h" 69#include "llvm/Operator.h" 70#include "llvm/Analysis/ConstantFolding.h" 71#include "llvm/Analysis/Dominators.h" 72#include "llvm/Analysis/InstructionSimplify.h" 73#include "llvm/Analysis/LoopInfo.h" 74#include "llvm/Analysis/ValueTracking.h" 75#include "llvm/Assembly/Writer.h" 76#include "llvm/Target/TargetData.h" 77#include "llvm/Support/CommandLine.h" 78#include "llvm/Support/ConstantRange.h" 79#include "llvm/Support/Debug.h" 80#include "llvm/Support/ErrorHandling.h" 81#include "llvm/Support/GetElementPtrTypeIterator.h" 82#include "llvm/Support/InstIterator.h" 83#include "llvm/Support/MathExtras.h" 84#include "llvm/Support/raw_ostream.h" 85#include "llvm/ADT/Statistic.h" 86#include "llvm/ADT/STLExtras.h" 87#include "llvm/ADT/SmallPtrSet.h" 88#include <algorithm> 89using namespace llvm; 90 91STATISTIC(NumArrayLenItCounts, 92 "Number of trip counts computed with array length"); 93STATISTIC(NumTripCountsComputed, 94 "Number of loops with predictable loop counts"); 95STATISTIC(NumTripCountsNotComputed, 96 "Number of loops without predictable loop counts"); 97STATISTIC(NumBruteForceTripCountsComputed, 98 "Number of loops with trip counts computed by force"); 99 100static cl::opt<unsigned> 101MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 102 cl::desc("Maximum number of iterations SCEV will " 103 "symbolically execute a constant " 104 "derived loop"), 105 cl::init(100)); 106 107INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution", 108 "Scalar Evolution Analysis", false, true) 109INITIALIZE_PASS_DEPENDENCY(LoopInfo) 110INITIALIZE_PASS_DEPENDENCY(DominatorTree) 111INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution", 112 "Scalar Evolution Analysis", false, true) 113char ScalarEvolution::ID = 0; 114 115//===----------------------------------------------------------------------===// 116// SCEV class definitions 117//===----------------------------------------------------------------------===// 118 119//===----------------------------------------------------------------------===// 120// Implementation of the SCEV class. 121// 122 123void SCEV::dump() const { 124 print(dbgs()); 125 dbgs() << '\n'; 126} 127 128void SCEV::print(raw_ostream &OS) const { 129 switch (getSCEVType()) { 130 case scConstant: 131 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false); 132 return; 133 case scTruncate: { 134 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this); 135 const SCEV *Op = Trunc->getOperand(); 136 OS << "(trunc " << *Op->getType() << " " << *Op << " to " 137 << *Trunc->getType() << ")"; 138 return; 139 } 140 case scZeroExtend: { 141 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this); 142 const SCEV *Op = ZExt->getOperand(); 143 OS << "(zext " << *Op->getType() << " " << *Op << " to " 144 << *ZExt->getType() << ")"; 145 return; 146 } 147 case scSignExtend: { 148 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this); 149 const SCEV *Op = SExt->getOperand(); 150 OS << "(sext " << *Op->getType() << " " << *Op << " to " 151 << *SExt->getType() << ")"; 152 return; 153 } 154 case scAddRecExpr: { 155 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this); 156 OS << "{" << *AR->getOperand(0); 157 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i) 158 OS << ",+," << *AR->getOperand(i); 159 OS << "}<"; 160 if (AR->hasNoUnsignedWrap()) 161 OS << "nuw><"; 162 if (AR->hasNoSignedWrap()) 163 OS << "nsw><"; 164 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false); 165 OS << ">"; 166 return; 167 } 168 case scAddExpr: 169 case scMulExpr: 170 case scUMaxExpr: 171 case scSMaxExpr: { 172 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this); 173 const char *OpStr = 0; 174 switch (NAry->getSCEVType()) { 175 case scAddExpr: OpStr = " + "; break; 176 case scMulExpr: OpStr = " * "; break; 177 case scUMaxExpr: OpStr = " umax "; break; 178 case scSMaxExpr: OpStr = " smax "; break; 179 } 180 OS << "("; 181 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 182 I != E; ++I) { 183 OS << **I; 184 if (llvm::next(I) != E) 185 OS << OpStr; 186 } 187 OS << ")"; 188 return; 189 } 190 case scUDivExpr: { 191 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this); 192 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")"; 193 return; 194 } 195 case scUnknown: { 196 const SCEVUnknown *U = cast<SCEVUnknown>(this); 197 const Type *AllocTy; 198 if (U->isSizeOf(AllocTy)) { 199 OS << "sizeof(" << *AllocTy << ")"; 200 return; 201 } 202 if (U->isAlignOf(AllocTy)) { 203 OS << "alignof(" << *AllocTy << ")"; 204 return; 205 } 206 207 const Type *CTy; 208 Constant *FieldNo; 209 if (U->isOffsetOf(CTy, FieldNo)) { 210 OS << "offsetof(" << *CTy << ", "; 211 WriteAsOperand(OS, FieldNo, false); 212 OS << ")"; 213 return; 214 } 215 216 // Otherwise just print it normally. 217 WriteAsOperand(OS, U->getValue(), false); 218 return; 219 } 220 case scCouldNotCompute: 221 OS << "***COULDNOTCOMPUTE***"; 222 return; 223 default: break; 224 } 225 llvm_unreachable("Unknown SCEV kind!"); 226} 227 228const Type *SCEV::getType() const { 229 switch (getSCEVType()) { 230 case scConstant: 231 return cast<SCEVConstant>(this)->getType(); 232 case scTruncate: 233 case scZeroExtend: 234 case scSignExtend: 235 return cast<SCEVCastExpr>(this)->getType(); 236 case scAddRecExpr: 237 case scMulExpr: 238 case scUMaxExpr: 239 case scSMaxExpr: 240 return cast<SCEVNAryExpr>(this)->getType(); 241 case scAddExpr: 242 return cast<SCEVAddExpr>(this)->getType(); 243 case scUDivExpr: 244 return cast<SCEVUDivExpr>(this)->getType(); 245 case scUnknown: 246 return cast<SCEVUnknown>(this)->getType(); 247 case scCouldNotCompute: 248 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 249 return 0; 250 default: break; 251 } 252 llvm_unreachable("Unknown SCEV kind!"); 253 return 0; 254} 255 256bool SCEV::isZero() const { 257 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 258 return SC->getValue()->isZero(); 259 return false; 260} 261 262bool SCEV::isOne() const { 263 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 264 return SC->getValue()->isOne(); 265 return false; 266} 267 268bool SCEV::isAllOnesValue() const { 269 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 270 return SC->getValue()->isAllOnesValue(); 271 return false; 272} 273 274SCEVCouldNotCompute::SCEVCouldNotCompute() : 275 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 276 277bool SCEVCouldNotCompute::classof(const SCEV *S) { 278 return S->getSCEVType() == scCouldNotCompute; 279} 280 281const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 282 FoldingSetNodeID ID; 283 ID.AddInteger(scConstant); 284 ID.AddPointer(V); 285 void *IP = 0; 286 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 287 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 288 UniqueSCEVs.InsertNode(S, IP); 289 return S; 290} 291 292const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 293 return getConstant(ConstantInt::get(getContext(), Val)); 294} 295 296const SCEV * 297ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 298 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 299 return getConstant(ConstantInt::get(ITy, V, isSigned)); 300} 301 302SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 303 unsigned SCEVTy, const SCEV *op, const Type *ty) 304 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 305 306SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 307 const SCEV *op, const Type *ty) 308 : SCEVCastExpr(ID, scTruncate, op, ty) { 309 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 310 (Ty->isIntegerTy() || Ty->isPointerTy()) && 311 "Cannot truncate non-integer value!"); 312} 313 314SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 315 const SCEV *op, const Type *ty) 316 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 317 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 318 (Ty->isIntegerTy() || Ty->isPointerTy()) && 319 "Cannot zero extend non-integer value!"); 320} 321 322SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 323 const SCEV *op, const Type *ty) 324 : SCEVCastExpr(ID, scSignExtend, op, ty) { 325 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 326 (Ty->isIntegerTy() || Ty->isPointerTy()) && 327 "Cannot sign extend non-integer value!"); 328} 329 330void SCEVUnknown::deleted() { 331 // Clear this SCEVUnknown from various maps. 332 SE->forgetMemoizedResults(this); 333 334 // Remove this SCEVUnknown from the uniquing map. 335 SE->UniqueSCEVs.RemoveNode(this); 336 337 // Release the value. 338 setValPtr(0); 339} 340 341void SCEVUnknown::allUsesReplacedWith(Value *New) { 342 // Clear this SCEVUnknown from various maps. 343 SE->forgetMemoizedResults(this); 344 345 // Remove this SCEVUnknown from the uniquing map. 346 SE->UniqueSCEVs.RemoveNode(this); 347 348 // Update this SCEVUnknown to point to the new value. This is needed 349 // because there may still be outstanding SCEVs which still point to 350 // this SCEVUnknown. 351 setValPtr(New); 352} 353 354bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { 355 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 356 if (VCE->getOpcode() == Instruction::PtrToInt) 357 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 358 if (CE->getOpcode() == Instruction::GetElementPtr && 359 CE->getOperand(0)->isNullValue() && 360 CE->getNumOperands() == 2) 361 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 362 if (CI->isOne()) { 363 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 364 ->getElementType(); 365 return true; 366 } 367 368 return false; 369} 370 371bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { 372 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 373 if (VCE->getOpcode() == Instruction::PtrToInt) 374 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 375 if (CE->getOpcode() == Instruction::GetElementPtr && 376 CE->getOperand(0)->isNullValue()) { 377 const Type *Ty = 378 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 379 if (const StructType *STy = dyn_cast<StructType>(Ty)) 380 if (!STy->isPacked() && 381 CE->getNumOperands() == 3 && 382 CE->getOperand(1)->isNullValue()) { 383 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 384 if (CI->isOne() && 385 STy->getNumElements() == 2 && 386 STy->getElementType(0)->isIntegerTy(1)) { 387 AllocTy = STy->getElementType(1); 388 return true; 389 } 390 } 391 } 392 393 return false; 394} 395 396bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { 397 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 398 if (VCE->getOpcode() == Instruction::PtrToInt) 399 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 400 if (CE->getOpcode() == Instruction::GetElementPtr && 401 CE->getNumOperands() == 3 && 402 CE->getOperand(0)->isNullValue() && 403 CE->getOperand(1)->isNullValue()) { 404 const Type *Ty = 405 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 406 // Ignore vector types here so that ScalarEvolutionExpander doesn't 407 // emit getelementptrs that index into vectors. 408 if (Ty->isStructTy() || Ty->isArrayTy()) { 409 CTy = Ty; 410 FieldNo = CE->getOperand(2); 411 return true; 412 } 413 } 414 415 return false; 416} 417 418//===----------------------------------------------------------------------===// 419// SCEV Utilities 420//===----------------------------------------------------------------------===// 421 422namespace { 423 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 424 /// than the complexity of the RHS. This comparator is used to canonicalize 425 /// expressions. 426 class SCEVComplexityCompare { 427 const LoopInfo *const LI; 428 public: 429 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 430 431 // Return true or false if LHS is less than, or at least RHS, respectively. 432 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 433 return compare(LHS, RHS) < 0; 434 } 435 436 // Return negative, zero, or positive, if LHS is less than, equal to, or 437 // greater than RHS, respectively. A three-way result allows recursive 438 // comparisons to be more efficient. 439 int compare(const SCEV *LHS, const SCEV *RHS) const { 440 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 441 if (LHS == RHS) 442 return 0; 443 444 // Primarily, sort the SCEVs by their getSCEVType(). 445 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 446 if (LType != RType) 447 return (int)LType - (int)RType; 448 449 // Aside from the getSCEVType() ordering, the particular ordering 450 // isn't very important except that it's beneficial to be consistent, 451 // so that (a + b) and (b + a) don't end up as different expressions. 452 switch (LType) { 453 case scUnknown: { 454 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 455 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 456 457 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 458 // not as complete as it could be. 459 const Value *LV = LU->getValue(), *RV = RU->getValue(); 460 461 // Order pointer values after integer values. This helps SCEVExpander 462 // form GEPs. 463 bool LIsPointer = LV->getType()->isPointerTy(), 464 RIsPointer = RV->getType()->isPointerTy(); 465 if (LIsPointer != RIsPointer) 466 return (int)LIsPointer - (int)RIsPointer; 467 468 // Compare getValueID values. 469 unsigned LID = LV->getValueID(), 470 RID = RV->getValueID(); 471 if (LID != RID) 472 return (int)LID - (int)RID; 473 474 // Sort arguments by their position. 475 if (const Argument *LA = dyn_cast<Argument>(LV)) { 476 const Argument *RA = cast<Argument>(RV); 477 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 478 return (int)LArgNo - (int)RArgNo; 479 } 480 481 // For instructions, compare their loop depth, and their operand 482 // count. This is pretty loose. 483 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) { 484 const Instruction *RInst = cast<Instruction>(RV); 485 486 // Compare loop depths. 487 const BasicBlock *LParent = LInst->getParent(), 488 *RParent = RInst->getParent(); 489 if (LParent != RParent) { 490 unsigned LDepth = LI->getLoopDepth(LParent), 491 RDepth = LI->getLoopDepth(RParent); 492 if (LDepth != RDepth) 493 return (int)LDepth - (int)RDepth; 494 } 495 496 // Compare the number of operands. 497 unsigned LNumOps = LInst->getNumOperands(), 498 RNumOps = RInst->getNumOperands(); 499 return (int)LNumOps - (int)RNumOps; 500 } 501 502 return 0; 503 } 504 505 case scConstant: { 506 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 507 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 508 509 // Compare constant values. 510 const APInt &LA = LC->getValue()->getValue(); 511 const APInt &RA = RC->getValue()->getValue(); 512 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 513 if (LBitWidth != RBitWidth) 514 return (int)LBitWidth - (int)RBitWidth; 515 return LA.ult(RA) ? -1 : 1; 516 } 517 518 case scAddRecExpr: { 519 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 520 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 521 522 // Compare addrec loop depths. 523 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 524 if (LLoop != RLoop) { 525 unsigned LDepth = LLoop->getLoopDepth(), 526 RDepth = RLoop->getLoopDepth(); 527 if (LDepth != RDepth) 528 return (int)LDepth - (int)RDepth; 529 } 530 531 // Addrec complexity grows with operand count. 532 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 533 if (LNumOps != RNumOps) 534 return (int)LNumOps - (int)RNumOps; 535 536 // Lexicographically compare. 537 for (unsigned i = 0; i != LNumOps; ++i) { 538 long X = compare(LA->getOperand(i), RA->getOperand(i)); 539 if (X != 0) 540 return X; 541 } 542 543 return 0; 544 } 545 546 case scAddExpr: 547 case scMulExpr: 548 case scSMaxExpr: 549 case scUMaxExpr: { 550 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 551 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 552 553 // Lexicographically compare n-ary expressions. 554 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 555 for (unsigned i = 0; i != LNumOps; ++i) { 556 if (i >= RNumOps) 557 return 1; 558 long X = compare(LC->getOperand(i), RC->getOperand(i)); 559 if (X != 0) 560 return X; 561 } 562 return (int)LNumOps - (int)RNumOps; 563 } 564 565 case scUDivExpr: { 566 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 567 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 568 569 // Lexicographically compare udiv expressions. 570 long X = compare(LC->getLHS(), RC->getLHS()); 571 if (X != 0) 572 return X; 573 return compare(LC->getRHS(), RC->getRHS()); 574 } 575 576 case scTruncate: 577 case scZeroExtend: 578 case scSignExtend: { 579 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 580 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 581 582 // Compare cast expressions by operand. 583 return compare(LC->getOperand(), RC->getOperand()); 584 } 585 586 default: 587 break; 588 } 589 590 llvm_unreachable("Unknown SCEV kind!"); 591 return 0; 592 } 593 }; 594} 595 596/// GroupByComplexity - Given a list of SCEV objects, order them by their 597/// complexity, and group objects of the same complexity together by value. 598/// When this routine is finished, we know that any duplicates in the vector are 599/// consecutive and that complexity is monotonically increasing. 600/// 601/// Note that we go take special precautions to ensure that we get deterministic 602/// results from this routine. In other words, we don't want the results of 603/// this to depend on where the addresses of various SCEV objects happened to 604/// land in memory. 605/// 606static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 607 LoopInfo *LI) { 608 if (Ops.size() < 2) return; // Noop 609 if (Ops.size() == 2) { 610 // This is the common case, which also happens to be trivially simple. 611 // Special case it. 612 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 613 if (SCEVComplexityCompare(LI)(RHS, LHS)) 614 std::swap(LHS, RHS); 615 return; 616 } 617 618 // Do the rough sort by complexity. 619 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 620 621 // Now that we are sorted by complexity, group elements of the same 622 // complexity. Note that this is, at worst, N^2, but the vector is likely to 623 // be extremely short in practice. Note that we take this approach because we 624 // do not want to depend on the addresses of the objects we are grouping. 625 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 626 const SCEV *S = Ops[i]; 627 unsigned Complexity = S->getSCEVType(); 628 629 // If there are any objects of the same complexity and same value as this 630 // one, group them. 631 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 632 if (Ops[j] == S) { // Found a duplicate. 633 // Move it to immediately after i'th element. 634 std::swap(Ops[i+1], Ops[j]); 635 ++i; // no need to rescan it. 636 if (i == e-2) return; // Done! 637 } 638 } 639 } 640} 641 642 643 644//===----------------------------------------------------------------------===// 645// Simple SCEV method implementations 646//===----------------------------------------------------------------------===// 647 648/// BinomialCoefficient - Compute BC(It, K). The result has width W. 649/// Assume, K > 0. 650static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 651 ScalarEvolution &SE, 652 const Type* ResultTy) { 653 // Handle the simplest case efficiently. 654 if (K == 1) 655 return SE.getTruncateOrZeroExtend(It, ResultTy); 656 657 // We are using the following formula for BC(It, K): 658 // 659 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 660 // 661 // Suppose, W is the bitwidth of the return value. We must be prepared for 662 // overflow. Hence, we must assure that the result of our computation is 663 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 664 // safe in modular arithmetic. 665 // 666 // However, this code doesn't use exactly that formula; the formula it uses 667 // is something like the following, where T is the number of factors of 2 in 668 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 669 // exponentiation: 670 // 671 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 672 // 673 // This formula is trivially equivalent to the previous formula. However, 674 // this formula can be implemented much more efficiently. The trick is that 675 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 676 // arithmetic. To do exact division in modular arithmetic, all we have 677 // to do is multiply by the inverse. Therefore, this step can be done at 678 // width W. 679 // 680 // The next issue is how to safely do the division by 2^T. The way this 681 // is done is by doing the multiplication step at a width of at least W + T 682 // bits. This way, the bottom W+T bits of the product are accurate. Then, 683 // when we perform the division by 2^T (which is equivalent to a right shift 684 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 685 // truncated out after the division by 2^T. 686 // 687 // In comparison to just directly using the first formula, this technique 688 // is much more efficient; using the first formula requires W * K bits, 689 // but this formula less than W + K bits. Also, the first formula requires 690 // a division step, whereas this formula only requires multiplies and shifts. 691 // 692 // It doesn't matter whether the subtraction step is done in the calculation 693 // width or the input iteration count's width; if the subtraction overflows, 694 // the result must be zero anyway. We prefer here to do it in the width of 695 // the induction variable because it helps a lot for certain cases; CodeGen 696 // isn't smart enough to ignore the overflow, which leads to much less 697 // efficient code if the width of the subtraction is wider than the native 698 // register width. 699 // 700 // (It's possible to not widen at all by pulling out factors of 2 before 701 // the multiplication; for example, K=2 can be calculated as 702 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 703 // extra arithmetic, so it's not an obvious win, and it gets 704 // much more complicated for K > 3.) 705 706 // Protection from insane SCEVs; this bound is conservative, 707 // but it probably doesn't matter. 708 if (K > 1000) 709 return SE.getCouldNotCompute(); 710 711 unsigned W = SE.getTypeSizeInBits(ResultTy); 712 713 // Calculate K! / 2^T and T; we divide out the factors of two before 714 // multiplying for calculating K! / 2^T to avoid overflow. 715 // Other overflow doesn't matter because we only care about the bottom 716 // W bits of the result. 717 APInt OddFactorial(W, 1); 718 unsigned T = 1; 719 for (unsigned i = 3; i <= K; ++i) { 720 APInt Mult(W, i); 721 unsigned TwoFactors = Mult.countTrailingZeros(); 722 T += TwoFactors; 723 Mult = Mult.lshr(TwoFactors); 724 OddFactorial *= Mult; 725 } 726 727 // We need at least W + T bits for the multiplication step 728 unsigned CalculationBits = W + T; 729 730 // Calculate 2^T, at width T+W. 731 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 732 733 // Calculate the multiplicative inverse of K! / 2^T; 734 // this multiplication factor will perform the exact division by 735 // K! / 2^T. 736 APInt Mod = APInt::getSignedMinValue(W+1); 737 APInt MultiplyFactor = OddFactorial.zext(W+1); 738 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 739 MultiplyFactor = MultiplyFactor.trunc(W); 740 741 // Calculate the product, at width T+W 742 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 743 CalculationBits); 744 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 745 for (unsigned i = 1; i != K; ++i) { 746 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 747 Dividend = SE.getMulExpr(Dividend, 748 SE.getTruncateOrZeroExtend(S, CalculationTy)); 749 } 750 751 // Divide by 2^T 752 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 753 754 // Truncate the result, and divide by K! / 2^T. 755 756 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 757 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 758} 759 760/// evaluateAtIteration - Return the value of this chain of recurrences at 761/// the specified iteration number. We can evaluate this recurrence by 762/// multiplying each element in the chain by the binomial coefficient 763/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 764/// 765/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 766/// 767/// where BC(It, k) stands for binomial coefficient. 768/// 769const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 770 ScalarEvolution &SE) const { 771 const SCEV *Result = getStart(); 772 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 773 // The computation is correct in the face of overflow provided that the 774 // multiplication is performed _after_ the evaluation of the binomial 775 // coefficient. 776 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 777 if (isa<SCEVCouldNotCompute>(Coeff)) 778 return Coeff; 779 780 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 781 } 782 return Result; 783} 784 785//===----------------------------------------------------------------------===// 786// SCEV Expression folder implementations 787//===----------------------------------------------------------------------===// 788 789const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 790 const Type *Ty) { 791 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 792 "This is not a truncating conversion!"); 793 assert(isSCEVable(Ty) && 794 "This is not a conversion to a SCEVable type!"); 795 Ty = getEffectiveSCEVType(Ty); 796 797 FoldingSetNodeID ID; 798 ID.AddInteger(scTruncate); 799 ID.AddPointer(Op); 800 ID.AddPointer(Ty); 801 void *IP = 0; 802 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 803 804 // Fold if the operand is constant. 805 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 806 return getConstant( 807 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), 808 getEffectiveSCEVType(Ty)))); 809 810 // trunc(trunc(x)) --> trunc(x) 811 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 812 return getTruncateExpr(ST->getOperand(), Ty); 813 814 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 815 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 816 return getTruncateOrSignExtend(SS->getOperand(), Ty); 817 818 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 819 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 820 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 821 822 // If the input value is a chrec scev, truncate the chrec's operands. 823 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 824 SmallVector<const SCEV *, 4> Operands; 825 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 826 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 827 return getAddRecExpr(Operands, AddRec->getLoop()); 828 } 829 830 // As a special case, fold trunc(undef) to undef. We don't want to 831 // know too much about SCEVUnknowns, but this special case is handy 832 // and harmless. 833 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 834 if (isa<UndefValue>(U->getValue())) 835 return getSCEV(UndefValue::get(Ty)); 836 837 // The cast wasn't folded; create an explicit cast node. We can reuse 838 // the existing insert position since if we get here, we won't have 839 // made any changes which would invalidate it. 840 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 841 Op, Ty); 842 UniqueSCEVs.InsertNode(S, IP); 843 return S; 844} 845 846const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 847 const Type *Ty) { 848 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 849 "This is not an extending conversion!"); 850 assert(isSCEVable(Ty) && 851 "This is not a conversion to a SCEVable type!"); 852 Ty = getEffectiveSCEVType(Ty); 853 854 // Fold if the operand is constant. 855 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 856 return getConstant( 857 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), 858 getEffectiveSCEVType(Ty)))); 859 860 // zext(zext(x)) --> zext(x) 861 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 862 return getZeroExtendExpr(SZ->getOperand(), Ty); 863 864 // Before doing any expensive analysis, check to see if we've already 865 // computed a SCEV for this Op and Ty. 866 FoldingSetNodeID ID; 867 ID.AddInteger(scZeroExtend); 868 ID.AddPointer(Op); 869 ID.AddPointer(Ty); 870 void *IP = 0; 871 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 872 873 // If the input value is a chrec scev, and we can prove that the value 874 // did not overflow the old, smaller, value, we can zero extend all of the 875 // operands (often constants). This allows analysis of something like 876 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 877 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 878 if (AR->isAffine()) { 879 const SCEV *Start = AR->getStart(); 880 const SCEV *Step = AR->getStepRecurrence(*this); 881 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 882 const Loop *L = AR->getLoop(); 883 884 // If we have special knowledge that this addrec won't overflow, 885 // we don't need to do any further analysis. 886 if (AR->hasNoUnsignedWrap()) 887 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 888 getZeroExtendExpr(Step, Ty), 889 L); 890 891 // Check whether the backedge-taken count is SCEVCouldNotCompute. 892 // Note that this serves two purposes: It filters out loops that are 893 // simply not analyzable, and it covers the case where this code is 894 // being called from within backedge-taken count analysis, such that 895 // attempting to ask for the backedge-taken count would likely result 896 // in infinite recursion. In the later case, the analysis code will 897 // cope with a conservative value, and it will take care to purge 898 // that value once it has finished. 899 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 900 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 901 // Manually compute the final value for AR, checking for 902 // overflow. 903 904 // Check whether the backedge-taken count can be losslessly casted to 905 // the addrec's type. The count is always unsigned. 906 const SCEV *CastedMaxBECount = 907 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 908 const SCEV *RecastedMaxBECount = 909 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 910 if (MaxBECount == RecastedMaxBECount) { 911 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 912 // Check whether Start+Step*MaxBECount has no unsigned overflow. 913 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 914 const SCEV *Add = getAddExpr(Start, ZMul); 915 const SCEV *OperandExtendedAdd = 916 getAddExpr(getZeroExtendExpr(Start, WideTy), 917 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 918 getZeroExtendExpr(Step, WideTy))); 919 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 920 // Return the expression with the addrec on the outside. 921 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 922 getZeroExtendExpr(Step, Ty), 923 L); 924 925 // Similar to above, only this time treat the step value as signed. 926 // This covers loops that count down. 927 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 928 Add = getAddExpr(Start, SMul); 929 OperandExtendedAdd = 930 getAddExpr(getZeroExtendExpr(Start, WideTy), 931 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 932 getSignExtendExpr(Step, WideTy))); 933 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 934 // Return the expression with the addrec on the outside. 935 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 936 getSignExtendExpr(Step, Ty), 937 L); 938 } 939 940 // If the backedge is guarded by a comparison with the pre-inc value 941 // the addrec is safe. Also, if the entry is guarded by a comparison 942 // with the start value and the backedge is guarded by a comparison 943 // with the post-inc value, the addrec is safe. 944 if (isKnownPositive(Step)) { 945 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 946 getUnsignedRange(Step).getUnsignedMax()); 947 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 948 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 949 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 950 AR->getPostIncExpr(*this), N))) 951 // Return the expression with the addrec on the outside. 952 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 953 getZeroExtendExpr(Step, Ty), 954 L); 955 } else if (isKnownNegative(Step)) { 956 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 957 getSignedRange(Step).getSignedMin()); 958 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 959 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 960 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 961 AR->getPostIncExpr(*this), N))) 962 // Return the expression with the addrec on the outside. 963 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 964 getSignExtendExpr(Step, Ty), 965 L); 966 } 967 } 968 } 969 970 // The cast wasn't folded; create an explicit cast node. 971 // Recompute the insert position, as it may have been invalidated. 972 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 973 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 974 Op, Ty); 975 UniqueSCEVs.InsertNode(S, IP); 976 return S; 977} 978 979const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 980 const Type *Ty) { 981 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 982 "This is not an extending conversion!"); 983 assert(isSCEVable(Ty) && 984 "This is not a conversion to a SCEVable type!"); 985 Ty = getEffectiveSCEVType(Ty); 986 987 // Fold if the operand is constant. 988 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 989 return getConstant( 990 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 991 getEffectiveSCEVType(Ty)))); 992 993 // sext(sext(x)) --> sext(x) 994 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 995 return getSignExtendExpr(SS->getOperand(), Ty); 996 997 // Before doing any expensive analysis, check to see if we've already 998 // computed a SCEV for this Op and Ty. 999 FoldingSetNodeID ID; 1000 ID.AddInteger(scSignExtend); 1001 ID.AddPointer(Op); 1002 ID.AddPointer(Ty); 1003 void *IP = 0; 1004 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1005 1006 // If the input value is a chrec scev, and we can prove that the value 1007 // did not overflow the old, smaller, value, we can sign extend all of the 1008 // operands (often constants). This allows analysis of something like 1009 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1010 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1011 if (AR->isAffine()) { 1012 const SCEV *Start = AR->getStart(); 1013 const SCEV *Step = AR->getStepRecurrence(*this); 1014 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1015 const Loop *L = AR->getLoop(); 1016 1017 // If we have special knowledge that this addrec won't overflow, 1018 // we don't need to do any further analysis. 1019 if (AR->hasNoSignedWrap()) 1020 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1021 getSignExtendExpr(Step, Ty), 1022 L); 1023 1024 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1025 // Note that this serves two purposes: It filters out loops that are 1026 // simply not analyzable, and it covers the case where this code is 1027 // being called from within backedge-taken count analysis, such that 1028 // attempting to ask for the backedge-taken count would likely result 1029 // in infinite recursion. In the later case, the analysis code will 1030 // cope with a conservative value, and it will take care to purge 1031 // that value once it has finished. 1032 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1033 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1034 // Manually compute the final value for AR, checking for 1035 // overflow. 1036 1037 // Check whether the backedge-taken count can be losslessly casted to 1038 // the addrec's type. The count is always unsigned. 1039 const SCEV *CastedMaxBECount = 1040 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1041 const SCEV *RecastedMaxBECount = 1042 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1043 if (MaxBECount == RecastedMaxBECount) { 1044 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1045 // Check whether Start+Step*MaxBECount has no signed overflow. 1046 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1047 const SCEV *Add = getAddExpr(Start, SMul); 1048 const SCEV *OperandExtendedAdd = 1049 getAddExpr(getSignExtendExpr(Start, WideTy), 1050 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1051 getSignExtendExpr(Step, WideTy))); 1052 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1053 // Return the expression with the addrec on the outside. 1054 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1055 getSignExtendExpr(Step, Ty), 1056 L); 1057 1058 // Similar to above, only this time treat the step value as unsigned. 1059 // This covers loops that count up with an unsigned step. 1060 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1061 Add = getAddExpr(Start, UMul); 1062 OperandExtendedAdd = 1063 getAddExpr(getSignExtendExpr(Start, WideTy), 1064 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1065 getZeroExtendExpr(Step, WideTy))); 1066 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1067 // Return the expression with the addrec on the outside. 1068 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1069 getZeroExtendExpr(Step, Ty), 1070 L); 1071 } 1072 1073 // If the backedge is guarded by a comparison with the pre-inc value 1074 // the addrec is safe. Also, if the entry is guarded by a comparison 1075 // with the start value and the backedge is guarded by a comparison 1076 // with the post-inc value, the addrec is safe. 1077 if (isKnownPositive(Step)) { 1078 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1079 getSignedRange(Step).getSignedMax()); 1080 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1081 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1082 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1083 AR->getPostIncExpr(*this), N))) 1084 // Return the expression with the addrec on the outside. 1085 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1086 getSignExtendExpr(Step, Ty), 1087 L); 1088 } else if (isKnownNegative(Step)) { 1089 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1090 getSignedRange(Step).getSignedMin()); 1091 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1092 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1093 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1094 AR->getPostIncExpr(*this), N))) 1095 // Return the expression with the addrec on the outside. 1096 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1097 getSignExtendExpr(Step, Ty), 1098 L); 1099 } 1100 } 1101 } 1102 1103 // The cast wasn't folded; create an explicit cast node. 1104 // Recompute the insert position, as it may have been invalidated. 1105 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1106 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1107 Op, Ty); 1108 UniqueSCEVs.InsertNode(S, IP); 1109 return S; 1110} 1111 1112/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1113/// unspecified bits out to the given type. 1114/// 1115const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1116 const Type *Ty) { 1117 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1118 "This is not an extending conversion!"); 1119 assert(isSCEVable(Ty) && 1120 "This is not a conversion to a SCEVable type!"); 1121 Ty = getEffectiveSCEVType(Ty); 1122 1123 // Sign-extend negative constants. 1124 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1125 if (SC->getValue()->getValue().isNegative()) 1126 return getSignExtendExpr(Op, Ty); 1127 1128 // Peel off a truncate cast. 1129 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1130 const SCEV *NewOp = T->getOperand(); 1131 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1132 return getAnyExtendExpr(NewOp, Ty); 1133 return getTruncateOrNoop(NewOp, Ty); 1134 } 1135 1136 // Next try a zext cast. If the cast is folded, use it. 1137 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1138 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1139 return ZExt; 1140 1141 // Next try a sext cast. If the cast is folded, use it. 1142 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1143 if (!isa<SCEVSignExtendExpr>(SExt)) 1144 return SExt; 1145 1146 // Force the cast to be folded into the operands of an addrec. 1147 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1148 SmallVector<const SCEV *, 4> Ops; 1149 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1150 I != E; ++I) 1151 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1152 return getAddRecExpr(Ops, AR->getLoop()); 1153 } 1154 1155 // As a special case, fold anyext(undef) to undef. We don't want to 1156 // know too much about SCEVUnknowns, but this special case is handy 1157 // and harmless. 1158 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1159 if (isa<UndefValue>(U->getValue())) 1160 return getSCEV(UndefValue::get(Ty)); 1161 1162 // If the expression is obviously signed, use the sext cast value. 1163 if (isa<SCEVSMaxExpr>(Op)) 1164 return SExt; 1165 1166 // Absent any other information, use the zext cast value. 1167 return ZExt; 1168} 1169 1170/// CollectAddOperandsWithScales - Process the given Ops list, which is 1171/// a list of operands to be added under the given scale, update the given 1172/// map. This is a helper function for getAddRecExpr. As an example of 1173/// what it does, given a sequence of operands that would form an add 1174/// expression like this: 1175/// 1176/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1177/// 1178/// where A and B are constants, update the map with these values: 1179/// 1180/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1181/// 1182/// and add 13 + A*B*29 to AccumulatedConstant. 1183/// This will allow getAddRecExpr to produce this: 1184/// 1185/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1186/// 1187/// This form often exposes folding opportunities that are hidden in 1188/// the original operand list. 1189/// 1190/// Return true iff it appears that any interesting folding opportunities 1191/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1192/// the common case where no interesting opportunities are present, and 1193/// is also used as a check to avoid infinite recursion. 1194/// 1195static bool 1196CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1197 SmallVector<const SCEV *, 8> &NewOps, 1198 APInt &AccumulatedConstant, 1199 const SCEV *const *Ops, size_t NumOperands, 1200 const APInt &Scale, 1201 ScalarEvolution &SE) { 1202 bool Interesting = false; 1203 1204 // Iterate over the add operands. They are sorted, with constants first. 1205 unsigned i = 0; 1206 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1207 ++i; 1208 // Pull a buried constant out to the outside. 1209 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1210 Interesting = true; 1211 AccumulatedConstant += Scale * C->getValue()->getValue(); 1212 } 1213 1214 // Next comes everything else. We're especially interested in multiplies 1215 // here, but they're in the middle, so just visit the rest with one loop. 1216 for (; i != NumOperands; ++i) { 1217 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1218 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1219 APInt NewScale = 1220 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1221 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1222 // A multiplication of a constant with another add; recurse. 1223 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1224 Interesting |= 1225 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1226 Add->op_begin(), Add->getNumOperands(), 1227 NewScale, SE); 1228 } else { 1229 // A multiplication of a constant with some other value. Update 1230 // the map. 1231 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1232 const SCEV *Key = SE.getMulExpr(MulOps); 1233 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1234 M.insert(std::make_pair(Key, NewScale)); 1235 if (Pair.second) { 1236 NewOps.push_back(Pair.first->first); 1237 } else { 1238 Pair.first->second += NewScale; 1239 // The map already had an entry for this value, which may indicate 1240 // a folding opportunity. 1241 Interesting = true; 1242 } 1243 } 1244 } else { 1245 // An ordinary operand. Update the map. 1246 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1247 M.insert(std::make_pair(Ops[i], Scale)); 1248 if (Pair.second) { 1249 NewOps.push_back(Pair.first->first); 1250 } else { 1251 Pair.first->second += Scale; 1252 // The map already had an entry for this value, which may indicate 1253 // a folding opportunity. 1254 Interesting = true; 1255 } 1256 } 1257 } 1258 1259 return Interesting; 1260} 1261 1262namespace { 1263 struct APIntCompare { 1264 bool operator()(const APInt &LHS, const APInt &RHS) const { 1265 return LHS.ult(RHS); 1266 } 1267 }; 1268} 1269 1270/// getAddExpr - Get a canonical add expression, or something simpler if 1271/// possible. 1272const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1273 bool HasNUW, bool HasNSW) { 1274 assert(!Ops.empty() && "Cannot get empty add!"); 1275 if (Ops.size() == 1) return Ops[0]; 1276#ifndef NDEBUG 1277 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1278 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1279 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1280 "SCEVAddExpr operand types don't match!"); 1281#endif 1282 1283 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1284 if (!HasNUW && HasNSW) { 1285 bool All = true; 1286 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1287 E = Ops.end(); I != E; ++I) 1288 if (!isKnownNonNegative(*I)) { 1289 All = false; 1290 break; 1291 } 1292 if (All) HasNUW = true; 1293 } 1294 1295 // Sort by complexity, this groups all similar expression types together. 1296 GroupByComplexity(Ops, LI); 1297 1298 // If there are any constants, fold them together. 1299 unsigned Idx = 0; 1300 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1301 ++Idx; 1302 assert(Idx < Ops.size()); 1303 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1304 // We found two constants, fold them together! 1305 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1306 RHSC->getValue()->getValue()); 1307 if (Ops.size() == 2) return Ops[0]; 1308 Ops.erase(Ops.begin()+1); // Erase the folded element 1309 LHSC = cast<SCEVConstant>(Ops[0]); 1310 } 1311 1312 // If we are left with a constant zero being added, strip it off. 1313 if (LHSC->getValue()->isZero()) { 1314 Ops.erase(Ops.begin()); 1315 --Idx; 1316 } 1317 1318 if (Ops.size() == 1) return Ops[0]; 1319 } 1320 1321 // Okay, check to see if the same value occurs in the operand list more than 1322 // once. If so, merge them together into an multiply expression. Since we 1323 // sorted the list, these values are required to be adjacent. 1324 const Type *Ty = Ops[0]->getType(); 1325 bool FoundMatch = false; 1326 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 1327 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1328 // Scan ahead to count how many equal operands there are. 1329 unsigned Count = 2; 1330 while (i+Count != e && Ops[i+Count] == Ops[i]) 1331 ++Count; 1332 // Merge the values into a multiply. 1333 const SCEV *Scale = getConstant(Ty, Count); 1334 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 1335 if (Ops.size() == Count) 1336 return Mul; 1337 Ops[i] = Mul; 1338 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 1339 --i; e -= Count - 1; 1340 FoundMatch = true; 1341 } 1342 if (FoundMatch) 1343 return getAddExpr(Ops, HasNUW, HasNSW); 1344 1345 // Check for truncates. If all the operands are truncated from the same 1346 // type, see if factoring out the truncate would permit the result to be 1347 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1348 // if the contents of the resulting outer trunc fold to something simple. 1349 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1350 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1351 const Type *DstType = Trunc->getType(); 1352 const Type *SrcType = Trunc->getOperand()->getType(); 1353 SmallVector<const SCEV *, 8> LargeOps; 1354 bool Ok = true; 1355 // Check all the operands to see if they can be represented in the 1356 // source type of the truncate. 1357 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1358 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1359 if (T->getOperand()->getType() != SrcType) { 1360 Ok = false; 1361 break; 1362 } 1363 LargeOps.push_back(T->getOperand()); 1364 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1365 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1366 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1367 SmallVector<const SCEV *, 8> LargeMulOps; 1368 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1369 if (const SCEVTruncateExpr *T = 1370 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1371 if (T->getOperand()->getType() != SrcType) { 1372 Ok = false; 1373 break; 1374 } 1375 LargeMulOps.push_back(T->getOperand()); 1376 } else if (const SCEVConstant *C = 1377 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1378 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1379 } else { 1380 Ok = false; 1381 break; 1382 } 1383 } 1384 if (Ok) 1385 LargeOps.push_back(getMulExpr(LargeMulOps)); 1386 } else { 1387 Ok = false; 1388 break; 1389 } 1390 } 1391 if (Ok) { 1392 // Evaluate the expression in the larger type. 1393 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1394 // If it folds to something simple, use it. Otherwise, don't. 1395 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1396 return getTruncateExpr(Fold, DstType); 1397 } 1398 } 1399 1400 // Skip past any other cast SCEVs. 1401 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1402 ++Idx; 1403 1404 // If there are add operands they would be next. 1405 if (Idx < Ops.size()) { 1406 bool DeletedAdd = false; 1407 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1408 // If we have an add, expand the add operands onto the end of the operands 1409 // list. 1410 Ops.erase(Ops.begin()+Idx); 1411 Ops.append(Add->op_begin(), Add->op_end()); 1412 DeletedAdd = true; 1413 } 1414 1415 // If we deleted at least one add, we added operands to the end of the list, 1416 // and they are not necessarily sorted. Recurse to resort and resimplify 1417 // any operands we just acquired. 1418 if (DeletedAdd) 1419 return getAddExpr(Ops); 1420 } 1421 1422 // Skip over the add expression until we get to a multiply. 1423 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1424 ++Idx; 1425 1426 // Check to see if there are any folding opportunities present with 1427 // operands multiplied by constant values. 1428 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1429 uint64_t BitWidth = getTypeSizeInBits(Ty); 1430 DenseMap<const SCEV *, APInt> M; 1431 SmallVector<const SCEV *, 8> NewOps; 1432 APInt AccumulatedConstant(BitWidth, 0); 1433 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1434 Ops.data(), Ops.size(), 1435 APInt(BitWidth, 1), *this)) { 1436 // Some interesting folding opportunity is present, so its worthwhile to 1437 // re-generate the operands list. Group the operands by constant scale, 1438 // to avoid multiplying by the same constant scale multiple times. 1439 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1440 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1441 E = NewOps.end(); I != E; ++I) 1442 MulOpLists[M.find(*I)->second].push_back(*I); 1443 // Re-generate the operands list. 1444 Ops.clear(); 1445 if (AccumulatedConstant != 0) 1446 Ops.push_back(getConstant(AccumulatedConstant)); 1447 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1448 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1449 if (I->first != 0) 1450 Ops.push_back(getMulExpr(getConstant(I->first), 1451 getAddExpr(I->second))); 1452 if (Ops.empty()) 1453 return getConstant(Ty, 0); 1454 if (Ops.size() == 1) 1455 return Ops[0]; 1456 return getAddExpr(Ops); 1457 } 1458 } 1459 1460 // If we are adding something to a multiply expression, make sure the 1461 // something is not already an operand of the multiply. If so, merge it into 1462 // the multiply. 1463 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1464 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1465 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1466 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1467 if (isa<SCEVConstant>(MulOpSCEV)) 1468 continue; 1469 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1470 if (MulOpSCEV == Ops[AddOp]) { 1471 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1472 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1473 if (Mul->getNumOperands() != 2) { 1474 // If the multiply has more than two operands, we must get the 1475 // Y*Z term. 1476 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1477 Mul->op_begin()+MulOp); 1478 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1479 InnerMul = getMulExpr(MulOps); 1480 } 1481 const SCEV *One = getConstant(Ty, 1); 1482 const SCEV *AddOne = getAddExpr(One, InnerMul); 1483 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1484 if (Ops.size() == 2) return OuterMul; 1485 if (AddOp < Idx) { 1486 Ops.erase(Ops.begin()+AddOp); 1487 Ops.erase(Ops.begin()+Idx-1); 1488 } else { 1489 Ops.erase(Ops.begin()+Idx); 1490 Ops.erase(Ops.begin()+AddOp-1); 1491 } 1492 Ops.push_back(OuterMul); 1493 return getAddExpr(Ops); 1494 } 1495 1496 // Check this multiply against other multiplies being added together. 1497 for (unsigned OtherMulIdx = Idx+1; 1498 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1499 ++OtherMulIdx) { 1500 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1501 // If MulOp occurs in OtherMul, we can fold the two multiplies 1502 // together. 1503 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1504 OMulOp != e; ++OMulOp) 1505 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1506 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1507 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1508 if (Mul->getNumOperands() != 2) { 1509 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1510 Mul->op_begin()+MulOp); 1511 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1512 InnerMul1 = getMulExpr(MulOps); 1513 } 1514 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1515 if (OtherMul->getNumOperands() != 2) { 1516 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1517 OtherMul->op_begin()+OMulOp); 1518 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 1519 InnerMul2 = getMulExpr(MulOps); 1520 } 1521 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1522 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1523 if (Ops.size() == 2) return OuterMul; 1524 Ops.erase(Ops.begin()+Idx); 1525 Ops.erase(Ops.begin()+OtherMulIdx-1); 1526 Ops.push_back(OuterMul); 1527 return getAddExpr(Ops); 1528 } 1529 } 1530 } 1531 } 1532 1533 // If there are any add recurrences in the operands list, see if any other 1534 // added values are loop invariant. If so, we can fold them into the 1535 // recurrence. 1536 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1537 ++Idx; 1538 1539 // Scan over all recurrences, trying to fold loop invariants into them. 1540 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1541 // Scan all of the other operands to this add and add them to the vector if 1542 // they are loop invariant w.r.t. the recurrence. 1543 SmallVector<const SCEV *, 8> LIOps; 1544 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1545 const Loop *AddRecLoop = AddRec->getLoop(); 1546 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1547 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1548 LIOps.push_back(Ops[i]); 1549 Ops.erase(Ops.begin()+i); 1550 --i; --e; 1551 } 1552 1553 // If we found some loop invariants, fold them into the recurrence. 1554 if (!LIOps.empty()) { 1555 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1556 LIOps.push_back(AddRec->getStart()); 1557 1558 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1559 AddRec->op_end()); 1560 AddRecOps[0] = getAddExpr(LIOps); 1561 1562 // Build the new addrec. Propagate the NUW and NSW flags if both the 1563 // outer add and the inner addrec are guaranteed to have no overflow. 1564 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, 1565 HasNUW && AddRec->hasNoUnsignedWrap(), 1566 HasNSW && AddRec->hasNoSignedWrap()); 1567 1568 // If all of the other operands were loop invariant, we are done. 1569 if (Ops.size() == 1) return NewRec; 1570 1571 // Otherwise, add the folded AddRec by the non-liv parts. 1572 for (unsigned i = 0;; ++i) 1573 if (Ops[i] == AddRec) { 1574 Ops[i] = NewRec; 1575 break; 1576 } 1577 return getAddExpr(Ops); 1578 } 1579 1580 // Okay, if there weren't any loop invariants to be folded, check to see if 1581 // there are multiple AddRec's with the same loop induction variable being 1582 // added together. If so, we can fold them. 1583 for (unsigned OtherIdx = Idx+1; 1584 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1585 ++OtherIdx) 1586 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1587 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 1588 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1589 AddRec->op_end()); 1590 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1591 ++OtherIdx) 1592 if (const SCEVAddRecExpr *OtherAddRec = 1593 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1594 if (OtherAddRec->getLoop() == AddRecLoop) { 1595 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 1596 i != e; ++i) { 1597 if (i >= AddRecOps.size()) { 1598 AddRecOps.append(OtherAddRec->op_begin()+i, 1599 OtherAddRec->op_end()); 1600 break; 1601 } 1602 AddRecOps[i] = getAddExpr(AddRecOps[i], 1603 OtherAddRec->getOperand(i)); 1604 } 1605 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1606 } 1607 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop); 1608 return getAddExpr(Ops); 1609 } 1610 1611 // Otherwise couldn't fold anything into this recurrence. Move onto the 1612 // next one. 1613 } 1614 1615 // Okay, it looks like we really DO need an add expr. Check to see if we 1616 // already have one, otherwise create a new one. 1617 FoldingSetNodeID ID; 1618 ID.AddInteger(scAddExpr); 1619 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1620 ID.AddPointer(Ops[i]); 1621 void *IP = 0; 1622 SCEVAddExpr *S = 1623 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1624 if (!S) { 1625 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1626 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1627 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1628 O, Ops.size()); 1629 UniqueSCEVs.InsertNode(S, IP); 1630 } 1631 if (HasNUW) S->setHasNoUnsignedWrap(true); 1632 if (HasNSW) S->setHasNoSignedWrap(true); 1633 return S; 1634} 1635 1636/// getMulExpr - Get a canonical multiply expression, or something simpler if 1637/// possible. 1638const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1639 bool HasNUW, bool HasNSW) { 1640 assert(!Ops.empty() && "Cannot get empty mul!"); 1641 if (Ops.size() == 1) return Ops[0]; 1642#ifndef NDEBUG 1643 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1644 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1645 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1646 "SCEVMulExpr operand types don't match!"); 1647#endif 1648 1649 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1650 if (!HasNUW && HasNSW) { 1651 bool All = true; 1652 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1653 E = Ops.end(); I != E; ++I) 1654 if (!isKnownNonNegative(*I)) { 1655 All = false; 1656 break; 1657 } 1658 if (All) HasNUW = true; 1659 } 1660 1661 // Sort by complexity, this groups all similar expression types together. 1662 GroupByComplexity(Ops, LI); 1663 1664 // If there are any constants, fold them together. 1665 unsigned Idx = 0; 1666 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1667 1668 // C1*(C2+V) -> C1*C2 + C1*V 1669 if (Ops.size() == 2) 1670 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1671 if (Add->getNumOperands() == 2 && 1672 isa<SCEVConstant>(Add->getOperand(0))) 1673 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1674 getMulExpr(LHSC, Add->getOperand(1))); 1675 1676 ++Idx; 1677 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1678 // We found two constants, fold them together! 1679 ConstantInt *Fold = ConstantInt::get(getContext(), 1680 LHSC->getValue()->getValue() * 1681 RHSC->getValue()->getValue()); 1682 Ops[0] = getConstant(Fold); 1683 Ops.erase(Ops.begin()+1); // Erase the folded element 1684 if (Ops.size() == 1) return Ops[0]; 1685 LHSC = cast<SCEVConstant>(Ops[0]); 1686 } 1687 1688 // If we are left with a constant one being multiplied, strip it off. 1689 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1690 Ops.erase(Ops.begin()); 1691 --Idx; 1692 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1693 // If we have a multiply of zero, it will always be zero. 1694 return Ops[0]; 1695 } else if (Ops[0]->isAllOnesValue()) { 1696 // If we have a mul by -1 of an add, try distributing the -1 among the 1697 // add operands. 1698 if (Ops.size() == 2) 1699 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1700 SmallVector<const SCEV *, 4> NewOps; 1701 bool AnyFolded = false; 1702 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); 1703 I != E; ++I) { 1704 const SCEV *Mul = getMulExpr(Ops[0], *I); 1705 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1706 NewOps.push_back(Mul); 1707 } 1708 if (AnyFolded) 1709 return getAddExpr(NewOps); 1710 } 1711 } 1712 1713 if (Ops.size() == 1) 1714 return Ops[0]; 1715 } 1716 1717 // Skip over the add expression until we get to a multiply. 1718 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1719 ++Idx; 1720 1721 // If there are mul operands inline them all into this expression. 1722 if (Idx < Ops.size()) { 1723 bool DeletedMul = false; 1724 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1725 // If we have an mul, expand the mul operands onto the end of the operands 1726 // list. 1727 Ops.erase(Ops.begin()+Idx); 1728 Ops.append(Mul->op_begin(), Mul->op_end()); 1729 DeletedMul = true; 1730 } 1731 1732 // If we deleted at least one mul, we added operands to the end of the list, 1733 // and they are not necessarily sorted. Recurse to resort and resimplify 1734 // any operands we just acquired. 1735 if (DeletedMul) 1736 return getMulExpr(Ops); 1737 } 1738 1739 // If there are any add recurrences in the operands list, see if any other 1740 // added values are loop invariant. If so, we can fold them into the 1741 // recurrence. 1742 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1743 ++Idx; 1744 1745 // Scan over all recurrences, trying to fold loop invariants into them. 1746 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1747 // Scan all of the other operands to this mul and add them to the vector if 1748 // they are loop invariant w.r.t. the recurrence. 1749 SmallVector<const SCEV *, 8> LIOps; 1750 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1751 const Loop *AddRecLoop = AddRec->getLoop(); 1752 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1753 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1754 LIOps.push_back(Ops[i]); 1755 Ops.erase(Ops.begin()+i); 1756 --i; --e; 1757 } 1758 1759 // If we found some loop invariants, fold them into the recurrence. 1760 if (!LIOps.empty()) { 1761 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1762 SmallVector<const SCEV *, 4> NewOps; 1763 NewOps.reserve(AddRec->getNumOperands()); 1764 const SCEV *Scale = getMulExpr(LIOps); 1765 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1766 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1767 1768 // Build the new addrec. Propagate the NUW and NSW flags if both the 1769 // outer mul and the inner addrec are guaranteed to have no overflow. 1770 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, 1771 HasNUW && AddRec->hasNoUnsignedWrap(), 1772 HasNSW && AddRec->hasNoSignedWrap()); 1773 1774 // If all of the other operands were loop invariant, we are done. 1775 if (Ops.size() == 1) return NewRec; 1776 1777 // Otherwise, multiply the folded AddRec by the non-liv parts. 1778 for (unsigned i = 0;; ++i) 1779 if (Ops[i] == AddRec) { 1780 Ops[i] = NewRec; 1781 break; 1782 } 1783 return getMulExpr(Ops); 1784 } 1785 1786 // Okay, if there weren't any loop invariants to be folded, check to see if 1787 // there are multiple AddRec's with the same loop induction variable being 1788 // multiplied together. If so, we can fold them. 1789 for (unsigned OtherIdx = Idx+1; 1790 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1791 ++OtherIdx) 1792 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1793 // F * G, where F = {A,+,B}<L> and G = {C,+,D}<L> --> 1794 // {A*C,+,F*D + G*B + B*D}<L> 1795 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1796 ++OtherIdx) 1797 if (const SCEVAddRecExpr *OtherAddRec = 1798 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1799 if (OtherAddRec->getLoop() == AddRecLoop) { 1800 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1801 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart()); 1802 const SCEV *B = F->getStepRecurrence(*this); 1803 const SCEV *D = G->getStepRecurrence(*this); 1804 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1805 getMulExpr(G, B), 1806 getMulExpr(B, D)); 1807 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1808 F->getLoop()); 1809 if (Ops.size() == 2) return NewAddRec; 1810 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec); 1811 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1812 } 1813 return getMulExpr(Ops); 1814 } 1815 1816 // Otherwise couldn't fold anything into this recurrence. Move onto the 1817 // next one. 1818 } 1819 1820 // Okay, it looks like we really DO need an mul expr. Check to see if we 1821 // already have one, otherwise create a new one. 1822 FoldingSetNodeID ID; 1823 ID.AddInteger(scMulExpr); 1824 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1825 ID.AddPointer(Ops[i]); 1826 void *IP = 0; 1827 SCEVMulExpr *S = 1828 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1829 if (!S) { 1830 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1831 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1832 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 1833 O, Ops.size()); 1834 UniqueSCEVs.InsertNode(S, IP); 1835 } 1836 if (HasNUW) S->setHasNoUnsignedWrap(true); 1837 if (HasNSW) S->setHasNoSignedWrap(true); 1838 return S; 1839} 1840 1841/// getUDivExpr - Get a canonical unsigned division expression, or something 1842/// simpler if possible. 1843const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1844 const SCEV *RHS) { 1845 assert(getEffectiveSCEVType(LHS->getType()) == 1846 getEffectiveSCEVType(RHS->getType()) && 1847 "SCEVUDivExpr operand types don't match!"); 1848 1849 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1850 if (RHSC->getValue()->equalsInt(1)) 1851 return LHS; // X udiv 1 --> x 1852 // If the denominator is zero, the result of the udiv is undefined. Don't 1853 // try to analyze it, because the resolution chosen here may differ from 1854 // the resolution chosen in other parts of the compiler. 1855 if (!RHSC->getValue()->isZero()) { 1856 // Determine if the division can be folded into the operands of 1857 // its operands. 1858 // TODO: Generalize this to non-constants by using known-bits information. 1859 const Type *Ty = LHS->getType(); 1860 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1861 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 1862 // For non-power-of-two values, effectively round the value up to the 1863 // nearest power of two. 1864 if (!RHSC->getValue()->getValue().isPowerOf2()) 1865 ++MaxShiftAmt; 1866 const IntegerType *ExtTy = 1867 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1868 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1869 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1870 if (const SCEVConstant *Step = 1871 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1872 if (!Step->getValue()->getValue() 1873 .urem(RHSC->getValue()->getValue()) && 1874 getZeroExtendExpr(AR, ExtTy) == 1875 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1876 getZeroExtendExpr(Step, ExtTy), 1877 AR->getLoop())) { 1878 SmallVector<const SCEV *, 4> Operands; 1879 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1880 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1881 return getAddRecExpr(Operands, AR->getLoop()); 1882 } 1883 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1884 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1885 SmallVector<const SCEV *, 4> Operands; 1886 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1887 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1888 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1889 // Find an operand that's safely divisible. 1890 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1891 const SCEV *Op = M->getOperand(i); 1892 const SCEV *Div = getUDivExpr(Op, RHSC); 1893 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1894 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 1895 M->op_end()); 1896 Operands[i] = Div; 1897 return getMulExpr(Operands); 1898 } 1899 } 1900 } 1901 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1902 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1903 SmallVector<const SCEV *, 4> Operands; 1904 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1905 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1906 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1907 Operands.clear(); 1908 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1909 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1910 if (isa<SCEVUDivExpr>(Op) || 1911 getMulExpr(Op, RHS) != A->getOperand(i)) 1912 break; 1913 Operands.push_back(Op); 1914 } 1915 if (Operands.size() == A->getNumOperands()) 1916 return getAddExpr(Operands); 1917 } 1918 } 1919 1920 // Fold if both operands are constant. 1921 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1922 Constant *LHSCV = LHSC->getValue(); 1923 Constant *RHSCV = RHSC->getValue(); 1924 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1925 RHSCV))); 1926 } 1927 } 1928 } 1929 1930 FoldingSetNodeID ID; 1931 ID.AddInteger(scUDivExpr); 1932 ID.AddPointer(LHS); 1933 ID.AddPointer(RHS); 1934 void *IP = 0; 1935 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1936 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 1937 LHS, RHS); 1938 UniqueSCEVs.InsertNode(S, IP); 1939 return S; 1940} 1941 1942 1943/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1944/// Simplify the expression as much as possible. 1945const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1946 const SCEV *Step, const Loop *L, 1947 bool HasNUW, bool HasNSW) { 1948 SmallVector<const SCEV *, 4> Operands; 1949 Operands.push_back(Start); 1950 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1951 if (StepChrec->getLoop() == L) { 1952 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 1953 return getAddRecExpr(Operands, L); 1954 } 1955 1956 Operands.push_back(Step); 1957 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 1958} 1959 1960/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1961/// Simplify the expression as much as possible. 1962const SCEV * 1963ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1964 const Loop *L, 1965 bool HasNUW, bool HasNSW) { 1966 if (Operands.size() == 1) return Operands[0]; 1967#ifndef NDEBUG 1968 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 1969 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1970 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 1971 "SCEVAddRecExpr operand types don't match!"); 1972 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1973 assert(isLoopInvariant(Operands[i], L) && 1974 "SCEVAddRecExpr operand is not loop-invariant!"); 1975#endif 1976 1977 if (Operands.back()->isZero()) { 1978 Operands.pop_back(); 1979 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 1980 } 1981 1982 // It's tempting to want to call getMaxBackedgeTakenCount count here and 1983 // use that information to infer NUW and NSW flags. However, computing a 1984 // BE count requires calling getAddRecExpr, so we may not yet have a 1985 // meaningful BE count at this point (and if we don't, we'd be stuck 1986 // with a SCEVCouldNotCompute as the cached BE count). 1987 1988 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1989 if (!HasNUW && HasNSW) { 1990 bool All = true; 1991 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 1992 E = Operands.end(); I != E; ++I) 1993 if (!isKnownNonNegative(*I)) { 1994 All = false; 1995 break; 1996 } 1997 if (All) HasNUW = true; 1998 } 1999 2000 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2001 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2002 const Loop *NestedLoop = NestedAR->getLoop(); 2003 if (L->contains(NestedLoop) ? 2004 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2005 (!NestedLoop->contains(L) && 2006 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2007 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2008 NestedAR->op_end()); 2009 Operands[0] = NestedAR->getStart(); 2010 // AddRecs require their operands be loop-invariant with respect to their 2011 // loops. Don't perform this transformation if it would break this 2012 // requirement. 2013 bool AllInvariant = true; 2014 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2015 if (!isLoopInvariant(Operands[i], L)) { 2016 AllInvariant = false; 2017 break; 2018 } 2019 if (AllInvariant) { 2020 NestedOperands[0] = getAddRecExpr(Operands, L); 2021 AllInvariant = true; 2022 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2023 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) { 2024 AllInvariant = false; 2025 break; 2026 } 2027 if (AllInvariant) 2028 // Ok, both add recurrences are valid after the transformation. 2029 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2030 } 2031 // Reset Operands to its original state. 2032 Operands[0] = NestedAR; 2033 } 2034 } 2035 2036 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2037 // already have one, otherwise create a new one. 2038 FoldingSetNodeID ID; 2039 ID.AddInteger(scAddRecExpr); 2040 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2041 ID.AddPointer(Operands[i]); 2042 ID.AddPointer(L); 2043 void *IP = 0; 2044 SCEVAddRecExpr *S = 2045 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2046 if (!S) { 2047 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2048 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2049 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2050 O, Operands.size(), L); 2051 UniqueSCEVs.InsertNode(S, IP); 2052 } 2053 if (HasNUW) S->setHasNoUnsignedWrap(true); 2054 if (HasNSW) S->setHasNoSignedWrap(true); 2055 return S; 2056} 2057 2058const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2059 const SCEV *RHS) { 2060 SmallVector<const SCEV *, 2> Ops; 2061 Ops.push_back(LHS); 2062 Ops.push_back(RHS); 2063 return getSMaxExpr(Ops); 2064} 2065 2066const SCEV * 2067ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2068 assert(!Ops.empty() && "Cannot get empty smax!"); 2069 if (Ops.size() == 1) return Ops[0]; 2070#ifndef NDEBUG 2071 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2072 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2073 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2074 "SCEVSMaxExpr operand types don't match!"); 2075#endif 2076 2077 // Sort by complexity, this groups all similar expression types together. 2078 GroupByComplexity(Ops, LI); 2079 2080 // If there are any constants, fold them together. 2081 unsigned Idx = 0; 2082 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2083 ++Idx; 2084 assert(Idx < Ops.size()); 2085 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2086 // We found two constants, fold them together! 2087 ConstantInt *Fold = ConstantInt::get(getContext(), 2088 APIntOps::smax(LHSC->getValue()->getValue(), 2089 RHSC->getValue()->getValue())); 2090 Ops[0] = getConstant(Fold); 2091 Ops.erase(Ops.begin()+1); // Erase the folded element 2092 if (Ops.size() == 1) return Ops[0]; 2093 LHSC = cast<SCEVConstant>(Ops[0]); 2094 } 2095 2096 // If we are left with a constant minimum-int, strip it off. 2097 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2098 Ops.erase(Ops.begin()); 2099 --Idx; 2100 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2101 // If we have an smax with a constant maximum-int, it will always be 2102 // maximum-int. 2103 return Ops[0]; 2104 } 2105 2106 if (Ops.size() == 1) return Ops[0]; 2107 } 2108 2109 // Find the first SMax 2110 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2111 ++Idx; 2112 2113 // Check to see if one of the operands is an SMax. If so, expand its operands 2114 // onto our operand list, and recurse to simplify. 2115 if (Idx < Ops.size()) { 2116 bool DeletedSMax = false; 2117 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2118 Ops.erase(Ops.begin()+Idx); 2119 Ops.append(SMax->op_begin(), SMax->op_end()); 2120 DeletedSMax = true; 2121 } 2122 2123 if (DeletedSMax) 2124 return getSMaxExpr(Ops); 2125 } 2126 2127 // Okay, check to see if the same value occurs in the operand list twice. If 2128 // so, delete one. Since we sorted the list, these values are required to 2129 // be adjacent. 2130 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2131 // X smax Y smax Y --> X smax Y 2132 // X smax Y --> X, if X is always greater than Y 2133 if (Ops[i] == Ops[i+1] || 2134 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2135 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2136 --i; --e; 2137 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2138 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2139 --i; --e; 2140 } 2141 2142 if (Ops.size() == 1) return Ops[0]; 2143 2144 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2145 2146 // Okay, it looks like we really DO need an smax expr. Check to see if we 2147 // already have one, otherwise create a new one. 2148 FoldingSetNodeID ID; 2149 ID.AddInteger(scSMaxExpr); 2150 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2151 ID.AddPointer(Ops[i]); 2152 void *IP = 0; 2153 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2154 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2155 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2156 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2157 O, Ops.size()); 2158 UniqueSCEVs.InsertNode(S, IP); 2159 return S; 2160} 2161 2162const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2163 const SCEV *RHS) { 2164 SmallVector<const SCEV *, 2> Ops; 2165 Ops.push_back(LHS); 2166 Ops.push_back(RHS); 2167 return getUMaxExpr(Ops); 2168} 2169 2170const SCEV * 2171ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2172 assert(!Ops.empty() && "Cannot get empty umax!"); 2173 if (Ops.size() == 1) return Ops[0]; 2174#ifndef NDEBUG 2175 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2176 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2177 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2178 "SCEVUMaxExpr operand types don't match!"); 2179#endif 2180 2181 // Sort by complexity, this groups all similar expression types together. 2182 GroupByComplexity(Ops, LI); 2183 2184 // If there are any constants, fold them together. 2185 unsigned Idx = 0; 2186 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2187 ++Idx; 2188 assert(Idx < Ops.size()); 2189 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2190 // We found two constants, fold them together! 2191 ConstantInt *Fold = ConstantInt::get(getContext(), 2192 APIntOps::umax(LHSC->getValue()->getValue(), 2193 RHSC->getValue()->getValue())); 2194 Ops[0] = getConstant(Fold); 2195 Ops.erase(Ops.begin()+1); // Erase the folded element 2196 if (Ops.size() == 1) return Ops[0]; 2197 LHSC = cast<SCEVConstant>(Ops[0]); 2198 } 2199 2200 // If we are left with a constant minimum-int, strip it off. 2201 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2202 Ops.erase(Ops.begin()); 2203 --Idx; 2204 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2205 // If we have an umax with a constant maximum-int, it will always be 2206 // maximum-int. 2207 return Ops[0]; 2208 } 2209 2210 if (Ops.size() == 1) return Ops[0]; 2211 } 2212 2213 // Find the first UMax 2214 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2215 ++Idx; 2216 2217 // Check to see if one of the operands is a UMax. If so, expand its operands 2218 // onto our operand list, and recurse to simplify. 2219 if (Idx < Ops.size()) { 2220 bool DeletedUMax = false; 2221 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2222 Ops.erase(Ops.begin()+Idx); 2223 Ops.append(UMax->op_begin(), UMax->op_end()); 2224 DeletedUMax = true; 2225 } 2226 2227 if (DeletedUMax) 2228 return getUMaxExpr(Ops); 2229 } 2230 2231 // Okay, check to see if the same value occurs in the operand list twice. If 2232 // so, delete one. Since we sorted the list, these values are required to 2233 // be adjacent. 2234 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2235 // X umax Y umax Y --> X umax Y 2236 // X umax Y --> X, if X is always greater than Y 2237 if (Ops[i] == Ops[i+1] || 2238 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2239 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2240 --i; --e; 2241 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2242 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2243 --i; --e; 2244 } 2245 2246 if (Ops.size() == 1) return Ops[0]; 2247 2248 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2249 2250 // Okay, it looks like we really DO need a umax expr. Check to see if we 2251 // already have one, otherwise create a new one. 2252 FoldingSetNodeID ID; 2253 ID.AddInteger(scUMaxExpr); 2254 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2255 ID.AddPointer(Ops[i]); 2256 void *IP = 0; 2257 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2258 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2259 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2260 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2261 O, Ops.size()); 2262 UniqueSCEVs.InsertNode(S, IP); 2263 return S; 2264} 2265 2266const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2267 const SCEV *RHS) { 2268 // ~smax(~x, ~y) == smin(x, y). 2269 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2270} 2271 2272const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2273 const SCEV *RHS) { 2274 // ~umax(~x, ~y) == umin(x, y) 2275 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2276} 2277 2278const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2279 // If we have TargetData, we can bypass creating a target-independent 2280 // constant expression and then folding it back into a ConstantInt. 2281 // This is just a compile-time optimization. 2282 if (TD) 2283 return getConstant(TD->getIntPtrType(getContext()), 2284 TD->getTypeAllocSize(AllocTy)); 2285 2286 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2287 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2288 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2289 C = Folded; 2290 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2291 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2292} 2293 2294const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2295 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2296 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2297 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2298 C = Folded; 2299 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2300 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2301} 2302 2303const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2304 unsigned FieldNo) { 2305 // If we have TargetData, we can bypass creating a target-independent 2306 // constant expression and then folding it back into a ConstantInt. 2307 // This is just a compile-time optimization. 2308 if (TD) 2309 return getConstant(TD->getIntPtrType(getContext()), 2310 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2311 2312 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2313 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2314 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2315 C = Folded; 2316 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2317 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2318} 2319 2320const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2321 Constant *FieldNo) { 2322 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2323 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2324 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2325 C = Folded; 2326 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2327 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2328} 2329 2330const SCEV *ScalarEvolution::getUnknown(Value *V) { 2331 // Don't attempt to do anything other than create a SCEVUnknown object 2332 // here. createSCEV only calls getUnknown after checking for all other 2333 // interesting possibilities, and any other code that calls getUnknown 2334 // is doing so in order to hide a value from SCEV canonicalization. 2335 2336 FoldingSetNodeID ID; 2337 ID.AddInteger(scUnknown); 2338 ID.AddPointer(V); 2339 void *IP = 0; 2340 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2341 assert(cast<SCEVUnknown>(S)->getValue() == V && 2342 "Stale SCEVUnknown in uniquing map!"); 2343 return S; 2344 } 2345 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2346 FirstUnknown); 2347 FirstUnknown = cast<SCEVUnknown>(S); 2348 UniqueSCEVs.InsertNode(S, IP); 2349 return S; 2350} 2351 2352//===----------------------------------------------------------------------===// 2353// Basic SCEV Analysis and PHI Idiom Recognition Code 2354// 2355 2356/// isSCEVable - Test if values of the given type are analyzable within 2357/// the SCEV framework. This primarily includes integer types, and it 2358/// can optionally include pointer types if the ScalarEvolution class 2359/// has access to target-specific information. 2360bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2361 // Integers and pointers are always SCEVable. 2362 return Ty->isIntegerTy() || Ty->isPointerTy(); 2363} 2364 2365/// getTypeSizeInBits - Return the size in bits of the specified type, 2366/// for which isSCEVable must return true. 2367uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2368 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2369 2370 // If we have a TargetData, use it! 2371 if (TD) 2372 return TD->getTypeSizeInBits(Ty); 2373 2374 // Integer types have fixed sizes. 2375 if (Ty->isIntegerTy()) 2376 return Ty->getPrimitiveSizeInBits(); 2377 2378 // The only other support type is pointer. Without TargetData, conservatively 2379 // assume pointers are 64-bit. 2380 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2381 return 64; 2382} 2383 2384/// getEffectiveSCEVType - Return a type with the same bitwidth as 2385/// the given type and which represents how SCEV will treat the given 2386/// type, for which isSCEVable must return true. For pointer types, 2387/// this is the pointer-sized integer type. 2388const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2389 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2390 2391 if (Ty->isIntegerTy()) 2392 return Ty; 2393 2394 // The only other support type is pointer. 2395 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2396 if (TD) return TD->getIntPtrType(getContext()); 2397 2398 // Without TargetData, conservatively assume pointers are 64-bit. 2399 return Type::getInt64Ty(getContext()); 2400} 2401 2402const SCEV *ScalarEvolution::getCouldNotCompute() { 2403 return &CouldNotCompute; 2404} 2405 2406/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2407/// expression and create a new one. 2408const SCEV *ScalarEvolution::getSCEV(Value *V) { 2409 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2410 2411 ValueExprMapType::const_iterator I = ValueExprMap.find(V); 2412 if (I != ValueExprMap.end()) return I->second; 2413 const SCEV *S = createSCEV(V); 2414 2415 // The process of creating a SCEV for V may have caused other SCEVs 2416 // to have been created, so it's necessary to insert the new entry 2417 // from scratch, rather than trying to remember the insert position 2418 // above. 2419 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2420 return S; 2421} 2422 2423/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2424/// 2425const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2426 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2427 return getConstant( 2428 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2429 2430 const Type *Ty = V->getType(); 2431 Ty = getEffectiveSCEVType(Ty); 2432 return getMulExpr(V, 2433 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2434} 2435 2436/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2437const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2438 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2439 return getConstant( 2440 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2441 2442 const Type *Ty = V->getType(); 2443 Ty = getEffectiveSCEVType(Ty); 2444 const SCEV *AllOnes = 2445 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2446 return getMinusSCEV(AllOnes, V); 2447} 2448 2449/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2450/// 2451const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, 2452 bool HasNUW, bool HasNSW) { 2453 // Fast path: X - X --> 0. 2454 if (LHS == RHS) 2455 return getConstant(LHS->getType(), 0); 2456 2457 // X - Y --> X + -Y 2458 return getAddExpr(LHS, getNegativeSCEV(RHS), HasNUW, HasNSW); 2459} 2460 2461/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2462/// input value to the specified type. If the type must be extended, it is zero 2463/// extended. 2464const SCEV * 2465ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, const Type *Ty) { 2466 const Type *SrcTy = V->getType(); 2467 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2468 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2469 "Cannot truncate or zero extend with non-integer arguments!"); 2470 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2471 return V; // No conversion 2472 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2473 return getTruncateExpr(V, Ty); 2474 return getZeroExtendExpr(V, Ty); 2475} 2476 2477/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2478/// input value to the specified type. If the type must be extended, it is sign 2479/// extended. 2480const SCEV * 2481ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2482 const Type *Ty) { 2483 const Type *SrcTy = V->getType(); 2484 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2485 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2486 "Cannot truncate or zero extend with non-integer arguments!"); 2487 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2488 return V; // No conversion 2489 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2490 return getTruncateExpr(V, Ty); 2491 return getSignExtendExpr(V, Ty); 2492} 2493 2494/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2495/// input value to the specified type. If the type must be extended, it is zero 2496/// extended. The conversion must not be narrowing. 2497const SCEV * 2498ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2499 const Type *SrcTy = V->getType(); 2500 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2501 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2502 "Cannot noop or zero extend with non-integer arguments!"); 2503 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2504 "getNoopOrZeroExtend cannot truncate!"); 2505 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2506 return V; // No conversion 2507 return getZeroExtendExpr(V, Ty); 2508} 2509 2510/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2511/// input value to the specified type. If the type must be extended, it is sign 2512/// extended. The conversion must not be narrowing. 2513const SCEV * 2514ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2515 const Type *SrcTy = V->getType(); 2516 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2517 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2518 "Cannot noop or sign extend with non-integer arguments!"); 2519 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2520 "getNoopOrSignExtend cannot truncate!"); 2521 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2522 return V; // No conversion 2523 return getSignExtendExpr(V, Ty); 2524} 2525 2526/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2527/// the input value to the specified type. If the type must be extended, 2528/// it is extended with unspecified bits. The conversion must not be 2529/// narrowing. 2530const SCEV * 2531ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2532 const Type *SrcTy = V->getType(); 2533 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2534 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2535 "Cannot noop or any extend with non-integer arguments!"); 2536 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2537 "getNoopOrAnyExtend cannot truncate!"); 2538 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2539 return V; // No conversion 2540 return getAnyExtendExpr(V, Ty); 2541} 2542 2543/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2544/// input value to the specified type. The conversion must not be widening. 2545const SCEV * 2546ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2547 const Type *SrcTy = V->getType(); 2548 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2549 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2550 "Cannot truncate or noop with non-integer arguments!"); 2551 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2552 "getTruncateOrNoop cannot extend!"); 2553 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2554 return V; // No conversion 2555 return getTruncateExpr(V, Ty); 2556} 2557 2558/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2559/// the types using zero-extension, and then perform a umax operation 2560/// with them. 2561const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2562 const SCEV *RHS) { 2563 const SCEV *PromotedLHS = LHS; 2564 const SCEV *PromotedRHS = RHS; 2565 2566 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2567 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2568 else 2569 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2570 2571 return getUMaxExpr(PromotedLHS, PromotedRHS); 2572} 2573 2574/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2575/// the types using zero-extension, and then perform a umin operation 2576/// with them. 2577const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2578 const SCEV *RHS) { 2579 const SCEV *PromotedLHS = LHS; 2580 const SCEV *PromotedRHS = RHS; 2581 2582 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2583 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2584 else 2585 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2586 2587 return getUMinExpr(PromotedLHS, PromotedRHS); 2588} 2589 2590/// PushDefUseChildren - Push users of the given Instruction 2591/// onto the given Worklist. 2592static void 2593PushDefUseChildren(Instruction *I, 2594 SmallVectorImpl<Instruction *> &Worklist) { 2595 // Push the def-use children onto the Worklist stack. 2596 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2597 UI != UE; ++UI) 2598 Worklist.push_back(cast<Instruction>(*UI)); 2599} 2600 2601/// ForgetSymbolicValue - This looks up computed SCEV values for all 2602/// instructions that depend on the given instruction and removes them from 2603/// the ValueExprMapType map if they reference SymName. This is used during PHI 2604/// resolution. 2605void 2606ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2607 SmallVector<Instruction *, 16> Worklist; 2608 PushDefUseChildren(PN, Worklist); 2609 2610 SmallPtrSet<Instruction *, 8> Visited; 2611 Visited.insert(PN); 2612 while (!Worklist.empty()) { 2613 Instruction *I = Worklist.pop_back_val(); 2614 if (!Visited.insert(I)) continue; 2615 2616 ValueExprMapType::iterator It = 2617 ValueExprMap.find(static_cast<Value *>(I)); 2618 if (It != ValueExprMap.end()) { 2619 const SCEV *Old = It->second; 2620 2621 // Short-circuit the def-use traversal if the symbolic name 2622 // ceases to appear in expressions. 2623 if (Old != SymName && !hasOperand(Old, SymName)) 2624 continue; 2625 2626 // SCEVUnknown for a PHI either means that it has an unrecognized 2627 // structure, it's a PHI that's in the progress of being computed 2628 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2629 // additional loop trip count information isn't going to change anything. 2630 // In the second case, createNodeForPHI will perform the necessary 2631 // updates on its own when it gets to that point. In the third, we do 2632 // want to forget the SCEVUnknown. 2633 if (!isa<PHINode>(I) || 2634 !isa<SCEVUnknown>(Old) || 2635 (I != PN && Old == SymName)) { 2636 forgetMemoizedResults(Old); 2637 ValueExprMap.erase(It); 2638 } 2639 } 2640 2641 PushDefUseChildren(I, Worklist); 2642 } 2643} 2644 2645/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2646/// a loop header, making it a potential recurrence, or it doesn't. 2647/// 2648const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2649 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2650 if (L->getHeader() == PN->getParent()) { 2651 // The loop may have multiple entrances or multiple exits; we can analyze 2652 // this phi as an addrec if it has a unique entry value and a unique 2653 // backedge value. 2654 Value *BEValueV = 0, *StartValueV = 0; 2655 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2656 Value *V = PN->getIncomingValue(i); 2657 if (L->contains(PN->getIncomingBlock(i))) { 2658 if (!BEValueV) { 2659 BEValueV = V; 2660 } else if (BEValueV != V) { 2661 BEValueV = 0; 2662 break; 2663 } 2664 } else if (!StartValueV) { 2665 StartValueV = V; 2666 } else if (StartValueV != V) { 2667 StartValueV = 0; 2668 break; 2669 } 2670 } 2671 if (BEValueV && StartValueV) { 2672 // While we are analyzing this PHI node, handle its value symbolically. 2673 const SCEV *SymbolicName = getUnknown(PN); 2674 assert(ValueExprMap.find(PN) == ValueExprMap.end() && 2675 "PHI node already processed?"); 2676 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2677 2678 // Using this symbolic name for the PHI, analyze the value coming around 2679 // the back-edge. 2680 const SCEV *BEValue = getSCEV(BEValueV); 2681 2682 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2683 // has a special value for the first iteration of the loop. 2684 2685 // If the value coming around the backedge is an add with the symbolic 2686 // value we just inserted, then we found a simple induction variable! 2687 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2688 // If there is a single occurrence of the symbolic value, replace it 2689 // with a recurrence. 2690 unsigned FoundIndex = Add->getNumOperands(); 2691 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2692 if (Add->getOperand(i) == SymbolicName) 2693 if (FoundIndex == e) { 2694 FoundIndex = i; 2695 break; 2696 } 2697 2698 if (FoundIndex != Add->getNumOperands()) { 2699 // Create an add with everything but the specified operand. 2700 SmallVector<const SCEV *, 8> Ops; 2701 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2702 if (i != FoundIndex) 2703 Ops.push_back(Add->getOperand(i)); 2704 const SCEV *Accum = getAddExpr(Ops); 2705 2706 // This is not a valid addrec if the step amount is varying each 2707 // loop iteration, but is not itself an addrec in this loop. 2708 if (isLoopInvariant(Accum, L) || 2709 (isa<SCEVAddRecExpr>(Accum) && 2710 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2711 bool HasNUW = false; 2712 bool HasNSW = false; 2713 2714 // If the increment doesn't overflow, then neither the addrec nor 2715 // the post-increment will overflow. 2716 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2717 if (OBO->hasNoUnsignedWrap()) 2718 HasNUW = true; 2719 if (OBO->hasNoSignedWrap()) 2720 HasNSW = true; 2721 } else if (isa<GEPOperator>(BEValueV)) { 2722 // If the increment is a GEP, then we know it won't perform an 2723 // unsigned overflow, because the address space cannot be 2724 // wrapped around. 2725 HasNUW = true; 2726 } 2727 2728 const SCEV *StartVal = getSCEV(StartValueV); 2729 const SCEV *PHISCEV = 2730 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2731 2732 // Since the no-wrap flags are on the increment, they apply to the 2733 // post-incremented value as well. 2734 if (isLoopInvariant(Accum, L)) 2735 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2736 Accum, L, HasNUW, HasNSW); 2737 2738 // Okay, for the entire analysis of this edge we assumed the PHI 2739 // to be symbolic. We now need to go back and purge all of the 2740 // entries for the scalars that use the symbolic expression. 2741 ForgetSymbolicName(PN, SymbolicName); 2742 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2743 return PHISCEV; 2744 } 2745 } 2746 } else if (const SCEVAddRecExpr *AddRec = 2747 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2748 // Otherwise, this could be a loop like this: 2749 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2750 // In this case, j = {1,+,1} and BEValue is j. 2751 // Because the other in-value of i (0) fits the evolution of BEValue 2752 // i really is an addrec evolution. 2753 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2754 const SCEV *StartVal = getSCEV(StartValueV); 2755 2756 // If StartVal = j.start - j.stride, we can use StartVal as the 2757 // initial step of the addrec evolution. 2758 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2759 AddRec->getOperand(1))) { 2760 const SCEV *PHISCEV = 2761 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2762 2763 // Okay, for the entire analysis of this edge we assumed the PHI 2764 // to be symbolic. We now need to go back and purge all of the 2765 // entries for the scalars that use the symbolic expression. 2766 ForgetSymbolicName(PN, SymbolicName); 2767 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2768 return PHISCEV; 2769 } 2770 } 2771 } 2772 } 2773 } 2774 2775 // If the PHI has a single incoming value, follow that value, unless the 2776 // PHI's incoming blocks are in a different loop, in which case doing so 2777 // risks breaking LCSSA form. Instcombine would normally zap these, but 2778 // it doesn't have DominatorTree information, so it may miss cases. 2779 if (Value *V = SimplifyInstruction(PN, TD, DT)) 2780 if (LI->replacementPreservesLCSSAForm(PN, V)) 2781 return getSCEV(V); 2782 2783 // If it's not a loop phi, we can't handle it yet. 2784 return getUnknown(PN); 2785} 2786 2787/// createNodeForGEP - Expand GEP instructions into add and multiply 2788/// operations. This allows them to be analyzed by regular SCEV code. 2789/// 2790const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2791 2792 // Don't blindly transfer the inbounds flag from the GEP instruction to the 2793 // Add expression, because the Instruction may be guarded by control flow 2794 // and the no-overflow bits may not be valid for the expression in any 2795 // context. 2796 2797 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2798 Value *Base = GEP->getOperand(0); 2799 // Don't attempt to analyze GEPs over unsized objects. 2800 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2801 return getUnknown(GEP); 2802 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 2803 gep_type_iterator GTI = gep_type_begin(GEP); 2804 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 2805 E = GEP->op_end(); 2806 I != E; ++I) { 2807 Value *Index = *I; 2808 // Compute the (potentially symbolic) offset in bytes for this index. 2809 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2810 // For a struct, add the member offset. 2811 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2812 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 2813 2814 // Add the field offset to the running total offset. 2815 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 2816 } else { 2817 // For an array, add the element offset, explicitly scaled. 2818 const SCEV *ElementSize = getSizeOfExpr(*GTI); 2819 const SCEV *IndexS = getSCEV(Index); 2820 // Getelementptr indices are signed. 2821 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 2822 2823 // Multiply the index by the element size to compute the element offset. 2824 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize); 2825 2826 // Add the element offset to the running total offset. 2827 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2828 } 2829 } 2830 2831 // Get the SCEV for the GEP base. 2832 const SCEV *BaseS = getSCEV(Base); 2833 2834 // Add the total offset from all the GEP indices to the base. 2835 return getAddExpr(BaseS, TotalOffset); 2836} 2837 2838/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2839/// guaranteed to end in (at every loop iteration). It is, at the same time, 2840/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2841/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2842uint32_t 2843ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2844 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2845 return C->getValue()->getValue().countTrailingZeros(); 2846 2847 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2848 return std::min(GetMinTrailingZeros(T->getOperand()), 2849 (uint32_t)getTypeSizeInBits(T->getType())); 2850 2851 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2852 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2853 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2854 getTypeSizeInBits(E->getType()) : OpRes; 2855 } 2856 2857 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2858 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2859 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2860 getTypeSizeInBits(E->getType()) : OpRes; 2861 } 2862 2863 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2864 // The result is the min of all operands results. 2865 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2866 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2867 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2868 return MinOpRes; 2869 } 2870 2871 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2872 // The result is the sum of all operands results. 2873 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2874 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2875 for (unsigned i = 1, e = M->getNumOperands(); 2876 SumOpRes != BitWidth && i != e; ++i) 2877 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2878 BitWidth); 2879 return SumOpRes; 2880 } 2881 2882 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2883 // The result is the min of all operands results. 2884 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2885 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2886 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2887 return MinOpRes; 2888 } 2889 2890 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2891 // The result is the min of all operands results. 2892 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2893 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2894 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2895 return MinOpRes; 2896 } 2897 2898 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2899 // The result is the min of all operands results. 2900 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2901 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2902 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2903 return MinOpRes; 2904 } 2905 2906 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2907 // For a SCEVUnknown, ask ValueTracking. 2908 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2909 APInt Mask = APInt::getAllOnesValue(BitWidth); 2910 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2911 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2912 return Zeros.countTrailingOnes(); 2913 } 2914 2915 // SCEVUDivExpr 2916 return 0; 2917} 2918 2919/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2920/// 2921ConstantRange 2922ScalarEvolution::getUnsignedRange(const SCEV *S) { 2923 // See if we've computed this range already. 2924 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S); 2925 if (I != UnsignedRanges.end()) 2926 return I->second; 2927 2928 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2929 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue())); 2930 2931 unsigned BitWidth = getTypeSizeInBits(S->getType()); 2932 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 2933 2934 // If the value has known zeros, the maximum unsigned value will have those 2935 // known zeros as well. 2936 uint32_t TZ = GetMinTrailingZeros(S); 2937 if (TZ != 0) 2938 ConservativeResult = 2939 ConstantRange(APInt::getMinValue(BitWidth), 2940 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 2941 2942 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2943 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2944 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2945 X = X.add(getUnsignedRange(Add->getOperand(i))); 2946 return setUnsignedRange(Add, ConservativeResult.intersectWith(X)); 2947 } 2948 2949 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2950 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2951 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2952 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2953 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X)); 2954 } 2955 2956 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2957 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2958 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2959 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2960 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X)); 2961 } 2962 2963 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2964 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2965 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2966 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 2967 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X)); 2968 } 2969 2970 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2971 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 2972 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 2973 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 2974 } 2975 2976 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2977 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 2978 return setUnsignedRange(ZExt, 2979 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 2980 } 2981 2982 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2983 ConstantRange X = getUnsignedRange(SExt->getOperand()); 2984 return setUnsignedRange(SExt, 2985 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 2986 } 2987 2988 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2989 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 2990 return setUnsignedRange(Trunc, 2991 ConservativeResult.intersectWith(X.truncate(BitWidth))); 2992 } 2993 2994 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2995 // If there's no unsigned wrap, the value will never be less than its 2996 // initial value. 2997 if (AddRec->hasNoUnsignedWrap()) 2998 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 2999 if (!C->getValue()->isZero()) 3000 ConservativeResult = 3001 ConservativeResult.intersectWith( 3002 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3003 3004 // TODO: non-affine addrec 3005 if (AddRec->isAffine()) { 3006 const Type *Ty = AddRec->getType(); 3007 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3008 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3009 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3010 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3011 3012 const SCEV *Start = AddRec->getStart(); 3013 const SCEV *Step = AddRec->getStepRecurrence(*this); 3014 3015 ConstantRange StartRange = getUnsignedRange(Start); 3016 ConstantRange StepRange = getSignedRange(Step); 3017 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3018 ConstantRange EndRange = 3019 StartRange.add(MaxBECountRange.multiply(StepRange)); 3020 3021 // Check for overflow. This must be done with ConstantRange arithmetic 3022 // because we could be called from within the ScalarEvolution overflow 3023 // checking code. 3024 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3025 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3026 ConstantRange ExtMaxBECountRange = 3027 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3028 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3029 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3030 ExtEndRange) 3031 return setUnsignedRange(AddRec, ConservativeResult); 3032 3033 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3034 EndRange.getUnsignedMin()); 3035 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3036 EndRange.getUnsignedMax()); 3037 if (Min.isMinValue() && Max.isMaxValue()) 3038 return setUnsignedRange(AddRec, ConservativeResult); 3039 return setUnsignedRange(AddRec, 3040 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3041 } 3042 } 3043 3044 return setUnsignedRange(AddRec, ConservativeResult); 3045 } 3046 3047 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3048 // For a SCEVUnknown, ask ValueTracking. 3049 APInt Mask = APInt::getAllOnesValue(BitWidth); 3050 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3051 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3052 if (Ones == ~Zeros + 1) 3053 return setUnsignedRange(U, ConservativeResult); 3054 return setUnsignedRange(U, 3055 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1))); 3056 } 3057 3058 return setUnsignedRange(S, ConservativeResult); 3059} 3060 3061/// getSignedRange - Determine the signed range for a particular SCEV. 3062/// 3063ConstantRange 3064ScalarEvolution::getSignedRange(const SCEV *S) { 3065 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S); 3066 if (I != SignedRanges.end()) 3067 return I->second; 3068 3069 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3070 return setSignedRange(C, ConstantRange(C->getValue()->getValue())); 3071 3072 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3073 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3074 3075 // If the value has known zeros, the maximum signed value will have those 3076 // known zeros as well. 3077 uint32_t TZ = GetMinTrailingZeros(S); 3078 if (TZ != 0) 3079 ConservativeResult = 3080 ConstantRange(APInt::getSignedMinValue(BitWidth), 3081 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3082 3083 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3084 ConstantRange X = getSignedRange(Add->getOperand(0)); 3085 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3086 X = X.add(getSignedRange(Add->getOperand(i))); 3087 return setSignedRange(Add, ConservativeResult.intersectWith(X)); 3088 } 3089 3090 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3091 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3092 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3093 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3094 return setSignedRange(Mul, ConservativeResult.intersectWith(X)); 3095 } 3096 3097 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3098 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3099 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3100 X = X.smax(getSignedRange(SMax->getOperand(i))); 3101 return setSignedRange(SMax, ConservativeResult.intersectWith(X)); 3102 } 3103 3104 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3105 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3106 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3107 X = X.umax(getSignedRange(UMax->getOperand(i))); 3108 return setSignedRange(UMax, ConservativeResult.intersectWith(X)); 3109 } 3110 3111 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3112 ConstantRange X = getSignedRange(UDiv->getLHS()); 3113 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3114 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3115 } 3116 3117 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3118 ConstantRange X = getSignedRange(ZExt->getOperand()); 3119 return setSignedRange(ZExt, 3120 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3121 } 3122 3123 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3124 ConstantRange X = getSignedRange(SExt->getOperand()); 3125 return setSignedRange(SExt, 3126 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3127 } 3128 3129 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3130 ConstantRange X = getSignedRange(Trunc->getOperand()); 3131 return setSignedRange(Trunc, 3132 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3133 } 3134 3135 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3136 // If there's no signed wrap, and all the operands have the same sign or 3137 // zero, the value won't ever change sign. 3138 if (AddRec->hasNoSignedWrap()) { 3139 bool AllNonNeg = true; 3140 bool AllNonPos = true; 3141 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3142 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3143 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3144 } 3145 if (AllNonNeg) 3146 ConservativeResult = ConservativeResult.intersectWith( 3147 ConstantRange(APInt(BitWidth, 0), 3148 APInt::getSignedMinValue(BitWidth))); 3149 else if (AllNonPos) 3150 ConservativeResult = ConservativeResult.intersectWith( 3151 ConstantRange(APInt::getSignedMinValue(BitWidth), 3152 APInt(BitWidth, 1))); 3153 } 3154 3155 // TODO: non-affine addrec 3156 if (AddRec->isAffine()) { 3157 const Type *Ty = AddRec->getType(); 3158 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3159 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3160 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3161 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3162 3163 const SCEV *Start = AddRec->getStart(); 3164 const SCEV *Step = AddRec->getStepRecurrence(*this); 3165 3166 ConstantRange StartRange = getSignedRange(Start); 3167 ConstantRange StepRange = getSignedRange(Step); 3168 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3169 ConstantRange EndRange = 3170 StartRange.add(MaxBECountRange.multiply(StepRange)); 3171 3172 // Check for overflow. This must be done with ConstantRange arithmetic 3173 // because we could be called from within the ScalarEvolution overflow 3174 // checking code. 3175 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3176 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3177 ConstantRange ExtMaxBECountRange = 3178 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3179 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3180 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3181 ExtEndRange) 3182 return setSignedRange(AddRec, ConservativeResult); 3183 3184 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3185 EndRange.getSignedMin()); 3186 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3187 EndRange.getSignedMax()); 3188 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3189 return setSignedRange(AddRec, ConservativeResult); 3190 return setSignedRange(AddRec, 3191 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3192 } 3193 } 3194 3195 return setSignedRange(AddRec, ConservativeResult); 3196 } 3197 3198 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3199 // For a SCEVUnknown, ask ValueTracking. 3200 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3201 return setSignedRange(U, ConservativeResult); 3202 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3203 if (NS == 1) 3204 return setSignedRange(U, ConservativeResult); 3205 return setSignedRange(U, ConservativeResult.intersectWith( 3206 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3207 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1))); 3208 } 3209 3210 return setSignedRange(S, ConservativeResult); 3211} 3212 3213/// createSCEV - We know that there is no SCEV for the specified value. 3214/// Analyze the expression. 3215/// 3216const SCEV *ScalarEvolution::createSCEV(Value *V) { 3217 if (!isSCEVable(V->getType())) 3218 return getUnknown(V); 3219 3220 unsigned Opcode = Instruction::UserOp1; 3221 if (Instruction *I = dyn_cast<Instruction>(V)) { 3222 Opcode = I->getOpcode(); 3223 3224 // Don't attempt to analyze instructions in blocks that aren't 3225 // reachable. Such instructions don't matter, and they aren't required 3226 // to obey basic rules for definitions dominating uses which this 3227 // analysis depends on. 3228 if (!DT->isReachableFromEntry(I->getParent())) 3229 return getUnknown(V); 3230 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3231 Opcode = CE->getOpcode(); 3232 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3233 return getConstant(CI); 3234 else if (isa<ConstantPointerNull>(V)) 3235 return getConstant(V->getType(), 0); 3236 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3237 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3238 else 3239 return getUnknown(V); 3240 3241 Operator *U = cast<Operator>(V); 3242 switch (Opcode) { 3243 case Instruction::Add: { 3244 // The simple thing to do would be to just call getSCEV on both operands 3245 // and call getAddExpr with the result. However if we're looking at a 3246 // bunch of things all added together, this can be quite inefficient, 3247 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3248 // Instead, gather up all the operands and make a single getAddExpr call. 3249 // LLVM IR canonical form means we need only traverse the left operands. 3250 SmallVector<const SCEV *, 4> AddOps; 3251 AddOps.push_back(getSCEV(U->getOperand(1))); 3252 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { 3253 unsigned Opcode = Op->getValueID() - Value::InstructionVal; 3254 if (Opcode != Instruction::Add && Opcode != Instruction::Sub) 3255 break; 3256 U = cast<Operator>(Op); 3257 const SCEV *Op1 = getSCEV(U->getOperand(1)); 3258 if (Opcode == Instruction::Sub) 3259 AddOps.push_back(getNegativeSCEV(Op1)); 3260 else 3261 AddOps.push_back(Op1); 3262 } 3263 AddOps.push_back(getSCEV(U->getOperand(0))); 3264 return getAddExpr(AddOps); 3265 } 3266 case Instruction::Mul: { 3267 // See the Add code above. 3268 SmallVector<const SCEV *, 4> MulOps; 3269 MulOps.push_back(getSCEV(U->getOperand(1))); 3270 for (Value *Op = U->getOperand(0); 3271 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3272 Op = U->getOperand(0)) { 3273 U = cast<Operator>(Op); 3274 MulOps.push_back(getSCEV(U->getOperand(1))); 3275 } 3276 MulOps.push_back(getSCEV(U->getOperand(0))); 3277 return getMulExpr(MulOps); 3278 } 3279 case Instruction::UDiv: 3280 return getUDivExpr(getSCEV(U->getOperand(0)), 3281 getSCEV(U->getOperand(1))); 3282 case Instruction::Sub: 3283 return getMinusSCEV(getSCEV(U->getOperand(0)), 3284 getSCEV(U->getOperand(1))); 3285 case Instruction::And: 3286 // For an expression like x&255 that merely masks off the high bits, 3287 // use zext(trunc(x)) as the SCEV expression. 3288 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3289 if (CI->isNullValue()) 3290 return getSCEV(U->getOperand(1)); 3291 if (CI->isAllOnesValue()) 3292 return getSCEV(U->getOperand(0)); 3293 const APInt &A = CI->getValue(); 3294 3295 // Instcombine's ShrinkDemandedConstant may strip bits out of 3296 // constants, obscuring what would otherwise be a low-bits mask. 3297 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3298 // knew about to reconstruct a low-bits mask value. 3299 unsigned LZ = A.countLeadingZeros(); 3300 unsigned BitWidth = A.getBitWidth(); 3301 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3302 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3303 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3304 3305 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3306 3307 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3308 return 3309 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3310 IntegerType::get(getContext(), BitWidth - LZ)), 3311 U->getType()); 3312 } 3313 break; 3314 3315 case Instruction::Or: 3316 // If the RHS of the Or is a constant, we may have something like: 3317 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3318 // optimizations will transparently handle this case. 3319 // 3320 // In order for this transformation to be safe, the LHS must be of the 3321 // form X*(2^n) and the Or constant must be less than 2^n. 3322 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3323 const SCEV *LHS = getSCEV(U->getOperand(0)); 3324 const APInt &CIVal = CI->getValue(); 3325 if (GetMinTrailingZeros(LHS) >= 3326 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3327 // Build a plain add SCEV. 3328 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3329 // If the LHS of the add was an addrec and it has no-wrap flags, 3330 // transfer the no-wrap flags, since an or won't introduce a wrap. 3331 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3332 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3333 if (OldAR->hasNoUnsignedWrap()) 3334 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3335 if (OldAR->hasNoSignedWrap()) 3336 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3337 } 3338 return S; 3339 } 3340 } 3341 break; 3342 case Instruction::Xor: 3343 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3344 // If the RHS of the xor is a signbit, then this is just an add. 3345 // Instcombine turns add of signbit into xor as a strength reduction step. 3346 if (CI->getValue().isSignBit()) 3347 return getAddExpr(getSCEV(U->getOperand(0)), 3348 getSCEV(U->getOperand(1))); 3349 3350 // If the RHS of xor is -1, then this is a not operation. 3351 if (CI->isAllOnesValue()) 3352 return getNotSCEV(getSCEV(U->getOperand(0))); 3353 3354 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3355 // This is a variant of the check for xor with -1, and it handles 3356 // the case where instcombine has trimmed non-demanded bits out 3357 // of an xor with -1. 3358 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3359 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3360 if (BO->getOpcode() == Instruction::And && 3361 LCI->getValue() == CI->getValue()) 3362 if (const SCEVZeroExtendExpr *Z = 3363 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3364 const Type *UTy = U->getType(); 3365 const SCEV *Z0 = Z->getOperand(); 3366 const Type *Z0Ty = Z0->getType(); 3367 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3368 3369 // If C is a low-bits mask, the zero extend is serving to 3370 // mask off the high bits. Complement the operand and 3371 // re-apply the zext. 3372 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3373 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3374 3375 // If C is a single bit, it may be in the sign-bit position 3376 // before the zero-extend. In this case, represent the xor 3377 // using an add, which is equivalent, and re-apply the zext. 3378 APInt Trunc = CI->getValue().trunc(Z0TySize); 3379 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3380 Trunc.isSignBit()) 3381 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3382 UTy); 3383 } 3384 } 3385 break; 3386 3387 case Instruction::Shl: 3388 // Turn shift left of a constant amount into a multiply. 3389 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3390 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3391 3392 // If the shift count is not less than the bitwidth, the result of 3393 // the shift is undefined. Don't try to analyze it, because the 3394 // resolution chosen here may differ from the resolution chosen in 3395 // other parts of the compiler. 3396 if (SA->getValue().uge(BitWidth)) 3397 break; 3398 3399 Constant *X = ConstantInt::get(getContext(), 3400 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3401 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3402 } 3403 break; 3404 3405 case Instruction::LShr: 3406 // Turn logical shift right of a constant into a unsigned divide. 3407 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3408 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3409 3410 // If the shift count is not less than the bitwidth, the result of 3411 // the shift is undefined. Don't try to analyze it, because the 3412 // resolution chosen here may differ from the resolution chosen in 3413 // other parts of the compiler. 3414 if (SA->getValue().uge(BitWidth)) 3415 break; 3416 3417 Constant *X = ConstantInt::get(getContext(), 3418 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3419 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3420 } 3421 break; 3422 3423 case Instruction::AShr: 3424 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3425 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3426 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3427 if (L->getOpcode() == Instruction::Shl && 3428 L->getOperand(1) == U->getOperand(1)) { 3429 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3430 3431 // If the shift count is not less than the bitwidth, the result of 3432 // the shift is undefined. Don't try to analyze it, because the 3433 // resolution chosen here may differ from the resolution chosen in 3434 // other parts of the compiler. 3435 if (CI->getValue().uge(BitWidth)) 3436 break; 3437 3438 uint64_t Amt = BitWidth - CI->getZExtValue(); 3439 if (Amt == BitWidth) 3440 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3441 return 3442 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3443 IntegerType::get(getContext(), 3444 Amt)), 3445 U->getType()); 3446 } 3447 break; 3448 3449 case Instruction::Trunc: 3450 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3451 3452 case Instruction::ZExt: 3453 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3454 3455 case Instruction::SExt: 3456 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3457 3458 case Instruction::BitCast: 3459 // BitCasts are no-op casts so we just eliminate the cast. 3460 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3461 return getSCEV(U->getOperand(0)); 3462 break; 3463 3464 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3465 // lead to pointer expressions which cannot safely be expanded to GEPs, 3466 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3467 // simplifying integer expressions. 3468 3469 case Instruction::GetElementPtr: 3470 return createNodeForGEP(cast<GEPOperator>(U)); 3471 3472 case Instruction::PHI: 3473 return createNodeForPHI(cast<PHINode>(U)); 3474 3475 case Instruction::Select: 3476 // This could be a smax or umax that was lowered earlier. 3477 // Try to recover it. 3478 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3479 Value *LHS = ICI->getOperand(0); 3480 Value *RHS = ICI->getOperand(1); 3481 switch (ICI->getPredicate()) { 3482 case ICmpInst::ICMP_SLT: 3483 case ICmpInst::ICMP_SLE: 3484 std::swap(LHS, RHS); 3485 // fall through 3486 case ICmpInst::ICMP_SGT: 3487 case ICmpInst::ICMP_SGE: 3488 // a >s b ? a+x : b+x -> smax(a, b)+x 3489 // a >s b ? b+x : a+x -> smin(a, b)+x 3490 if (LHS->getType() == U->getType()) { 3491 const SCEV *LS = getSCEV(LHS); 3492 const SCEV *RS = getSCEV(RHS); 3493 const SCEV *LA = getSCEV(U->getOperand(1)); 3494 const SCEV *RA = getSCEV(U->getOperand(2)); 3495 const SCEV *LDiff = getMinusSCEV(LA, LS); 3496 const SCEV *RDiff = getMinusSCEV(RA, RS); 3497 if (LDiff == RDiff) 3498 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3499 LDiff = getMinusSCEV(LA, RS); 3500 RDiff = getMinusSCEV(RA, LS); 3501 if (LDiff == RDiff) 3502 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3503 } 3504 break; 3505 case ICmpInst::ICMP_ULT: 3506 case ICmpInst::ICMP_ULE: 3507 std::swap(LHS, RHS); 3508 // fall through 3509 case ICmpInst::ICMP_UGT: 3510 case ICmpInst::ICMP_UGE: 3511 // a >u b ? a+x : b+x -> umax(a, b)+x 3512 // a >u b ? b+x : a+x -> umin(a, b)+x 3513 if (LHS->getType() == U->getType()) { 3514 const SCEV *LS = getSCEV(LHS); 3515 const SCEV *RS = getSCEV(RHS); 3516 const SCEV *LA = getSCEV(U->getOperand(1)); 3517 const SCEV *RA = getSCEV(U->getOperand(2)); 3518 const SCEV *LDiff = getMinusSCEV(LA, LS); 3519 const SCEV *RDiff = getMinusSCEV(RA, RS); 3520 if (LDiff == RDiff) 3521 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3522 LDiff = getMinusSCEV(LA, RS); 3523 RDiff = getMinusSCEV(RA, LS); 3524 if (LDiff == RDiff) 3525 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3526 } 3527 break; 3528 case ICmpInst::ICMP_NE: 3529 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3530 if (LHS->getType() == U->getType() && 3531 isa<ConstantInt>(RHS) && 3532 cast<ConstantInt>(RHS)->isZero()) { 3533 const SCEV *One = getConstant(LHS->getType(), 1); 3534 const SCEV *LS = getSCEV(LHS); 3535 const SCEV *LA = getSCEV(U->getOperand(1)); 3536 const SCEV *RA = getSCEV(U->getOperand(2)); 3537 const SCEV *LDiff = getMinusSCEV(LA, LS); 3538 const SCEV *RDiff = getMinusSCEV(RA, One); 3539 if (LDiff == RDiff) 3540 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3541 } 3542 break; 3543 case ICmpInst::ICMP_EQ: 3544 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3545 if (LHS->getType() == U->getType() && 3546 isa<ConstantInt>(RHS) && 3547 cast<ConstantInt>(RHS)->isZero()) { 3548 const SCEV *One = getConstant(LHS->getType(), 1); 3549 const SCEV *LS = getSCEV(LHS); 3550 const SCEV *LA = getSCEV(U->getOperand(1)); 3551 const SCEV *RA = getSCEV(U->getOperand(2)); 3552 const SCEV *LDiff = getMinusSCEV(LA, One); 3553 const SCEV *RDiff = getMinusSCEV(RA, LS); 3554 if (LDiff == RDiff) 3555 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3556 } 3557 break; 3558 default: 3559 break; 3560 } 3561 } 3562 3563 default: // We cannot analyze this expression. 3564 break; 3565 } 3566 3567 return getUnknown(V); 3568} 3569 3570 3571 3572//===----------------------------------------------------------------------===// 3573// Iteration Count Computation Code 3574// 3575 3576/// getBackedgeTakenCount - If the specified loop has a predictable 3577/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3578/// object. The backedge-taken count is the number of times the loop header 3579/// will be branched to from within the loop. This is one less than the 3580/// trip count of the loop, since it doesn't count the first iteration, 3581/// when the header is branched to from outside the loop. 3582/// 3583/// Note that it is not valid to call this method on a loop without a 3584/// loop-invariant backedge-taken count (see 3585/// hasLoopInvariantBackedgeTakenCount). 3586/// 3587const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3588 return getBackedgeTakenInfo(L).Exact; 3589} 3590 3591/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3592/// return the least SCEV value that is known never to be less than the 3593/// actual backedge taken count. 3594const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3595 return getBackedgeTakenInfo(L).Max; 3596} 3597 3598/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3599/// onto the given Worklist. 3600static void 3601PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3602 BasicBlock *Header = L->getHeader(); 3603 3604 // Push all Loop-header PHIs onto the Worklist stack. 3605 for (BasicBlock::iterator I = Header->begin(); 3606 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3607 Worklist.push_back(PN); 3608} 3609 3610const ScalarEvolution::BackedgeTakenInfo & 3611ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3612 // Initially insert a CouldNotCompute for this loop. If the insertion 3613 // succeeds, proceed to actually compute a backedge-taken count and 3614 // update the value. The temporary CouldNotCompute value tells SCEV 3615 // code elsewhere that it shouldn't attempt to request a new 3616 // backedge-taken count, which could result in infinite recursion. 3617 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3618 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3619 if (!Pair.second) 3620 return Pair.first->second; 3621 3622 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3623 if (BECount.Exact != getCouldNotCompute()) { 3624 assert(isLoopInvariant(BECount.Exact, L) && 3625 isLoopInvariant(BECount.Max, L) && 3626 "Computed backedge-taken count isn't loop invariant for loop!"); 3627 ++NumTripCountsComputed; 3628 3629 // Update the value in the map. 3630 Pair.first->second = BECount; 3631 } else { 3632 if (BECount.Max != getCouldNotCompute()) 3633 // Update the value in the map. 3634 Pair.first->second = BECount; 3635 if (isa<PHINode>(L->getHeader()->begin())) 3636 // Only count loops that have phi nodes as not being computable. 3637 ++NumTripCountsNotComputed; 3638 } 3639 3640 // Now that we know more about the trip count for this loop, forget any 3641 // existing SCEV values for PHI nodes in this loop since they are only 3642 // conservative estimates made without the benefit of trip count 3643 // information. This is similar to the code in forgetLoop, except that 3644 // it handles SCEVUnknown PHI nodes specially. 3645 if (BECount.hasAnyInfo()) { 3646 SmallVector<Instruction *, 16> Worklist; 3647 PushLoopPHIs(L, Worklist); 3648 3649 SmallPtrSet<Instruction *, 8> Visited; 3650 while (!Worklist.empty()) { 3651 Instruction *I = Worklist.pop_back_val(); 3652 if (!Visited.insert(I)) continue; 3653 3654 ValueExprMapType::iterator It = 3655 ValueExprMap.find(static_cast<Value *>(I)); 3656 if (It != ValueExprMap.end()) { 3657 const SCEV *Old = It->second; 3658 3659 // SCEVUnknown for a PHI either means that it has an unrecognized 3660 // structure, or it's a PHI that's in the progress of being computed 3661 // by createNodeForPHI. In the former case, additional loop trip 3662 // count information isn't going to change anything. In the later 3663 // case, createNodeForPHI will perform the necessary updates on its 3664 // own when it gets to that point. 3665 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) { 3666 forgetMemoizedResults(Old); 3667 ValueExprMap.erase(It); 3668 } 3669 if (PHINode *PN = dyn_cast<PHINode>(I)) 3670 ConstantEvolutionLoopExitValue.erase(PN); 3671 } 3672 3673 PushDefUseChildren(I, Worklist); 3674 } 3675 } 3676 return Pair.first->second; 3677} 3678 3679/// forgetLoop - This method should be called by the client when it has 3680/// changed a loop in a way that may effect ScalarEvolution's ability to 3681/// compute a trip count, or if the loop is deleted. 3682void ScalarEvolution::forgetLoop(const Loop *L) { 3683 // Drop any stored trip count value. 3684 BackedgeTakenCounts.erase(L); 3685 3686 // Drop information about expressions based on loop-header PHIs. 3687 SmallVector<Instruction *, 16> Worklist; 3688 PushLoopPHIs(L, Worklist); 3689 3690 SmallPtrSet<Instruction *, 8> Visited; 3691 while (!Worklist.empty()) { 3692 Instruction *I = Worklist.pop_back_val(); 3693 if (!Visited.insert(I)) continue; 3694 3695 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3696 if (It != ValueExprMap.end()) { 3697 forgetMemoizedResults(It->second); 3698 ValueExprMap.erase(It); 3699 if (PHINode *PN = dyn_cast<PHINode>(I)) 3700 ConstantEvolutionLoopExitValue.erase(PN); 3701 } 3702 3703 PushDefUseChildren(I, Worklist); 3704 } 3705 3706 // Forget all contained loops too, to avoid dangling entries in the 3707 // ValuesAtScopes map. 3708 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 3709 forgetLoop(*I); 3710} 3711 3712/// forgetValue - This method should be called by the client when it has 3713/// changed a value in a way that may effect its value, or which may 3714/// disconnect it from a def-use chain linking it to a loop. 3715void ScalarEvolution::forgetValue(Value *V) { 3716 Instruction *I = dyn_cast<Instruction>(V); 3717 if (!I) return; 3718 3719 // Drop information about expressions based on loop-header PHIs. 3720 SmallVector<Instruction *, 16> Worklist; 3721 Worklist.push_back(I); 3722 3723 SmallPtrSet<Instruction *, 8> Visited; 3724 while (!Worklist.empty()) { 3725 I = Worklist.pop_back_val(); 3726 if (!Visited.insert(I)) continue; 3727 3728 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3729 if (It != ValueExprMap.end()) { 3730 forgetMemoizedResults(It->second); 3731 ValueExprMap.erase(It); 3732 if (PHINode *PN = dyn_cast<PHINode>(I)) 3733 ConstantEvolutionLoopExitValue.erase(PN); 3734 } 3735 3736 PushDefUseChildren(I, Worklist); 3737 } 3738} 3739 3740/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3741/// of the specified loop will execute. 3742ScalarEvolution::BackedgeTakenInfo 3743ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3744 SmallVector<BasicBlock *, 8> ExitingBlocks; 3745 L->getExitingBlocks(ExitingBlocks); 3746 3747 // Examine all exits and pick the most conservative values. 3748 const SCEV *BECount = getCouldNotCompute(); 3749 const SCEV *MaxBECount = getCouldNotCompute(); 3750 bool CouldNotComputeBECount = false; 3751 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3752 BackedgeTakenInfo NewBTI = 3753 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3754 3755 if (NewBTI.Exact == getCouldNotCompute()) { 3756 // We couldn't compute an exact value for this exit, so 3757 // we won't be able to compute an exact value for the loop. 3758 CouldNotComputeBECount = true; 3759 BECount = getCouldNotCompute(); 3760 } else if (!CouldNotComputeBECount) { 3761 if (BECount == getCouldNotCompute()) 3762 BECount = NewBTI.Exact; 3763 else 3764 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3765 } 3766 if (MaxBECount == getCouldNotCompute()) 3767 MaxBECount = NewBTI.Max; 3768 else if (NewBTI.Max != getCouldNotCompute()) 3769 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3770 } 3771 3772 return BackedgeTakenInfo(BECount, MaxBECount); 3773} 3774 3775/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3776/// of the specified loop will execute if it exits via the specified block. 3777ScalarEvolution::BackedgeTakenInfo 3778ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3779 BasicBlock *ExitingBlock) { 3780 3781 // Okay, we've chosen an exiting block. See what condition causes us to 3782 // exit at this block. 3783 // 3784 // FIXME: we should be able to handle switch instructions (with a single exit) 3785 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3786 if (ExitBr == 0) return getCouldNotCompute(); 3787 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3788 3789 // At this point, we know we have a conditional branch that determines whether 3790 // the loop is exited. However, we don't know if the branch is executed each 3791 // time through the loop. If not, then the execution count of the branch will 3792 // not be equal to the trip count of the loop. 3793 // 3794 // Currently we check for this by checking to see if the Exit branch goes to 3795 // the loop header. If so, we know it will always execute the same number of 3796 // times as the loop. We also handle the case where the exit block *is* the 3797 // loop header. This is common for un-rotated loops. 3798 // 3799 // If both of those tests fail, walk up the unique predecessor chain to the 3800 // header, stopping if there is an edge that doesn't exit the loop. If the 3801 // header is reached, the execution count of the branch will be equal to the 3802 // trip count of the loop. 3803 // 3804 // More extensive analysis could be done to handle more cases here. 3805 // 3806 if (ExitBr->getSuccessor(0) != L->getHeader() && 3807 ExitBr->getSuccessor(1) != L->getHeader() && 3808 ExitBr->getParent() != L->getHeader()) { 3809 // The simple checks failed, try climbing the unique predecessor chain 3810 // up to the header. 3811 bool Ok = false; 3812 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3813 BasicBlock *Pred = BB->getUniquePredecessor(); 3814 if (!Pred) 3815 return getCouldNotCompute(); 3816 TerminatorInst *PredTerm = Pred->getTerminator(); 3817 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3818 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3819 if (PredSucc == BB) 3820 continue; 3821 // If the predecessor has a successor that isn't BB and isn't 3822 // outside the loop, assume the worst. 3823 if (L->contains(PredSucc)) 3824 return getCouldNotCompute(); 3825 } 3826 if (Pred == L->getHeader()) { 3827 Ok = true; 3828 break; 3829 } 3830 BB = Pred; 3831 } 3832 if (!Ok) 3833 return getCouldNotCompute(); 3834 } 3835 3836 // Proceed to the next level to examine the exit condition expression. 3837 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3838 ExitBr->getSuccessor(0), 3839 ExitBr->getSuccessor(1)); 3840} 3841 3842/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3843/// backedge of the specified loop will execute if its exit condition 3844/// were a conditional branch of ExitCond, TBB, and FBB. 3845ScalarEvolution::BackedgeTakenInfo 3846ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3847 Value *ExitCond, 3848 BasicBlock *TBB, 3849 BasicBlock *FBB) { 3850 // Check if the controlling expression for this loop is an And or Or. 3851 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3852 if (BO->getOpcode() == Instruction::And) { 3853 // Recurse on the operands of the and. 3854 BackedgeTakenInfo BTI0 = 3855 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3856 BackedgeTakenInfo BTI1 = 3857 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3858 const SCEV *BECount = getCouldNotCompute(); 3859 const SCEV *MaxBECount = getCouldNotCompute(); 3860 if (L->contains(TBB)) { 3861 // Both conditions must be true for the loop to continue executing. 3862 // Choose the less conservative count. 3863 if (BTI0.Exact == getCouldNotCompute() || 3864 BTI1.Exact == getCouldNotCompute()) 3865 BECount = getCouldNotCompute(); 3866 else 3867 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3868 if (BTI0.Max == getCouldNotCompute()) 3869 MaxBECount = BTI1.Max; 3870 else if (BTI1.Max == getCouldNotCompute()) 3871 MaxBECount = BTI0.Max; 3872 else 3873 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3874 } else { 3875 // Both conditions must be true at the same time for the loop to exit. 3876 // For now, be conservative. 3877 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3878 if (BTI0.Max == BTI1.Max) 3879 MaxBECount = BTI0.Max; 3880 if (BTI0.Exact == BTI1.Exact) 3881 BECount = BTI0.Exact; 3882 } 3883 3884 return BackedgeTakenInfo(BECount, MaxBECount); 3885 } 3886 if (BO->getOpcode() == Instruction::Or) { 3887 // Recurse on the operands of the or. 3888 BackedgeTakenInfo BTI0 = 3889 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3890 BackedgeTakenInfo BTI1 = 3891 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3892 const SCEV *BECount = getCouldNotCompute(); 3893 const SCEV *MaxBECount = getCouldNotCompute(); 3894 if (L->contains(FBB)) { 3895 // Both conditions must be false for the loop to continue executing. 3896 // Choose the less conservative count. 3897 if (BTI0.Exact == getCouldNotCompute() || 3898 BTI1.Exact == getCouldNotCompute()) 3899 BECount = getCouldNotCompute(); 3900 else 3901 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3902 if (BTI0.Max == getCouldNotCompute()) 3903 MaxBECount = BTI1.Max; 3904 else if (BTI1.Max == getCouldNotCompute()) 3905 MaxBECount = BTI0.Max; 3906 else 3907 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3908 } else { 3909 // Both conditions must be false at the same time for the loop to exit. 3910 // For now, be conservative. 3911 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3912 if (BTI0.Max == BTI1.Max) 3913 MaxBECount = BTI0.Max; 3914 if (BTI0.Exact == BTI1.Exact) 3915 BECount = BTI0.Exact; 3916 } 3917 3918 return BackedgeTakenInfo(BECount, MaxBECount); 3919 } 3920 } 3921 3922 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3923 // Proceed to the next level to examine the icmp. 3924 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3925 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3926 3927 // Check for a constant condition. These are normally stripped out by 3928 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 3929 // preserve the CFG and is temporarily leaving constant conditions 3930 // in place. 3931 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 3932 if (L->contains(FBB) == !CI->getZExtValue()) 3933 // The backedge is always taken. 3934 return getCouldNotCompute(); 3935 else 3936 // The backedge is never taken. 3937 return getConstant(CI->getType(), 0); 3938 } 3939 3940 // If it's not an integer or pointer comparison then compute it the hard way. 3941 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3942} 3943 3944static const SCEVAddRecExpr * 3945isSimpleUnwrappingAddRec(const SCEV *S, const Loop *L) { 3946 const SCEVAddRecExpr *SA = dyn_cast<SCEVAddRecExpr>(S); 3947 3948 // The SCEV must be an addrec of this loop. 3949 if (!SA || SA->getLoop() != L || !SA->isAffine()) 3950 return 0; 3951 3952 // The SCEV must be known to not wrap in some way to be interesting. 3953 if (!SA->hasNoUnsignedWrap() && !SA->hasNoSignedWrap()) 3954 return 0; 3955 3956 // The stride must be a constant so that we know if it is striding up or down. 3957 if (!isa<SCEVConstant>(SA->getOperand(1))) 3958 return 0; 3959 return SA; 3960} 3961 3962/// getMinusSCEVForExitTest - When considering an exit test for a loop with a 3963/// "x != y" exit test, we turn this into a computation that evaluates x-y != 0, 3964/// and this function returns the expression to use for x-y. We know and take 3965/// advantage of the fact that this subtraction is only being used in a 3966/// comparison by zero context. 3967/// 3968static const SCEV *getMinusSCEVForExitTest(const SCEV *LHS, const SCEV *RHS, 3969 const Loop *L, ScalarEvolution &SE) { 3970 // If either LHS or RHS is an AddRec SCEV (of this loop) that is known to not 3971 // wrap (either NSW or NUW), then we know that the value will either become 3972 // the other one (and thus the loop terminates), that the loop will terminate 3973 // through some other exit condition first, or that the loop has undefined 3974 // behavior. This information is useful when the addrec has a stride that is 3975 // != 1 or -1, because it means we can't "miss" the exit value. 3976 // 3977 // In any of these three cases, it is safe to turn the exit condition into a 3978 // "counting down" AddRec (to zero) by subtracting the two inputs as normal, 3979 // but since we know that the "end cannot be missed" we can force the 3980 // resulting AddRec to be a NUW addrec. Since it is counting down, this means 3981 // that the AddRec *cannot* pass zero. 3982 3983 // See if LHS and RHS are addrec's we can handle. 3984 const SCEVAddRecExpr *LHSA = isSimpleUnwrappingAddRec(LHS, L); 3985 const SCEVAddRecExpr *RHSA = isSimpleUnwrappingAddRec(RHS, L); 3986 3987 // If neither addrec is interesting, just return a minus. 3988 if (RHSA == 0 && LHSA == 0) 3989 return SE.getMinusSCEV(LHS, RHS); 3990 3991 // If only one of LHS and RHS are an AddRec of this loop, make sure it is LHS. 3992 if (RHSA && LHSA == 0) { 3993 // Safe because a-b === b-a for comparisons against zero. 3994 std::swap(LHS, RHS); 3995 std::swap(LHSA, RHSA); 3996 } 3997 3998 // Handle the case when only one is advancing in a non-overflowing way. 3999 if (RHSA == 0) { 4000 // If RHS is loop varying, then we can't predict when LHS will cross it. 4001 if (!SE.isLoopInvariant(RHS, L)) 4002 return SE.getMinusSCEV(LHS, RHS); 4003 4004 // If LHS has a positive stride, then we compute RHS-LHS, because the loop 4005 // is counting up until it crosses RHS (which must be larger than LHS). If 4006 // it is negative, we compute LHS-RHS because we're counting down to RHS. 4007 const ConstantInt *Stride = 4008 cast<SCEVConstant>(LHSA->getOperand(1))->getValue(); 4009 if (Stride->getValue().isNegative()) 4010 std::swap(LHS, RHS); 4011 4012 return SE.getMinusSCEV(RHS, LHS, true /*HasNUW*/); 4013 } 4014 4015 // If both LHS and RHS are interesting, we have something like: 4016 // a+i*4 != b+i*8. 4017 const ConstantInt *LHSStride = 4018 cast<SCEVConstant>(LHSA->getOperand(1))->getValue(); 4019 const ConstantInt *RHSStride = 4020 cast<SCEVConstant>(RHSA->getOperand(1))->getValue(); 4021 4022 // If the strides are equal, then this is just a (complex) loop invariant 4023 // comparison of a/b. 4024 if (LHSStride == RHSStride) 4025 return SE.getMinusSCEV(LHSA->getStart(), RHSA->getStart()); 4026 4027 // If the signs of the strides differ, then the negative stride is counting 4028 // down to the positive stride. 4029 if (LHSStride->getValue().isNegative() != RHSStride->getValue().isNegative()){ 4030 if (RHSStride->getValue().isNegative()) 4031 std::swap(LHS, RHS); 4032 } else { 4033 // If LHS's stride is smaller than RHS's stride, then "b" must be less than 4034 // "a" and "b" is RHS is counting up (catching up) to LHS. This is true 4035 // whether the strides are positive or negative. 4036 if (RHSStride->getValue().slt(LHSStride->getValue())) 4037 std::swap(LHS, RHS); 4038 } 4039 4040 return SE.getMinusSCEV(LHS, RHS, true /*HasNUW*/); 4041} 4042 4043/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 4044/// backedge of the specified loop will execute if its exit condition 4045/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4046ScalarEvolution::BackedgeTakenInfo 4047ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 4048 ICmpInst *ExitCond, 4049 BasicBlock *TBB, 4050 BasicBlock *FBB) { 4051 4052 // If the condition was exit on true, convert the condition to exit on false 4053 ICmpInst::Predicate Cond; 4054 if (!L->contains(FBB)) 4055 Cond = ExitCond->getPredicate(); 4056 else 4057 Cond = ExitCond->getInversePredicate(); 4058 4059 // Handle common loops like: for (X = "string"; *X; ++X) 4060 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4061 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4062 BackedgeTakenInfo ItCnt = 4063 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 4064 if (ItCnt.hasAnyInfo()) 4065 return ItCnt; 4066 } 4067 4068 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4069 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4070 4071 // Try to evaluate any dependencies out of the loop. 4072 LHS = getSCEVAtScope(LHS, L); 4073 RHS = getSCEVAtScope(RHS, L); 4074 4075 // At this point, we would like to compute how many iterations of the 4076 // loop the predicate will return true for these inputs. 4077 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) { 4078 // If there is a loop-invariant, force it into the RHS. 4079 std::swap(LHS, RHS); 4080 Cond = ICmpInst::getSwappedPredicate(Cond); 4081 } 4082 4083 // Simplify the operands before analyzing them. 4084 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4085 4086 // If we have a comparison of a chrec against a constant, try to use value 4087 // ranges to answer this query. 4088 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4089 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4090 if (AddRec->getLoop() == L) { 4091 // Form the constant range. 4092 ConstantRange CompRange( 4093 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4094 4095 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4096 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4097 } 4098 4099 switch (Cond) { 4100 case ICmpInst::ICMP_NE: { // while (X != Y) 4101 // Convert to: while (X-Y != 0) 4102 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEVForExitTest(LHS, RHS, L, 4103 *this), L); 4104 if (BTI.hasAnyInfo()) return BTI; 4105 break; 4106 } 4107 case ICmpInst::ICMP_EQ: { // while (X == Y) 4108 // Convert to: while (X-Y == 0) 4109 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4110 if (BTI.hasAnyInfo()) return BTI; 4111 break; 4112 } 4113 case ICmpInst::ICMP_SLT: { 4114 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 4115 if (BTI.hasAnyInfo()) return BTI; 4116 break; 4117 } 4118 case ICmpInst::ICMP_SGT: { 4119 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4120 getNotSCEV(RHS), L, true); 4121 if (BTI.hasAnyInfo()) return BTI; 4122 break; 4123 } 4124 case ICmpInst::ICMP_ULT: { 4125 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 4126 if (BTI.hasAnyInfo()) return BTI; 4127 break; 4128 } 4129 case ICmpInst::ICMP_UGT: { 4130 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4131 getNotSCEV(RHS), L, false); 4132 if (BTI.hasAnyInfo()) return BTI; 4133 break; 4134 } 4135 default: 4136#if 0 4137 dbgs() << "ComputeBackedgeTakenCount "; 4138 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4139 dbgs() << "[unsigned] "; 4140 dbgs() << *LHS << " " 4141 << Instruction::getOpcodeName(Instruction::ICmp) 4142 << " " << *RHS << "\n"; 4143#endif 4144 break; 4145 } 4146 return 4147 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4148} 4149 4150static ConstantInt * 4151EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4152 ScalarEvolution &SE) { 4153 const SCEV *InVal = SE.getConstant(C); 4154 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4155 assert(isa<SCEVConstant>(Val) && 4156 "Evaluation of SCEV at constant didn't fold correctly?"); 4157 return cast<SCEVConstant>(Val)->getValue(); 4158} 4159 4160/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4161/// and a GEP expression (missing the pointer index) indexing into it, return 4162/// the addressed element of the initializer or null if the index expression is 4163/// invalid. 4164static Constant * 4165GetAddressedElementFromGlobal(GlobalVariable *GV, 4166 const std::vector<ConstantInt*> &Indices) { 4167 Constant *Init = GV->getInitializer(); 4168 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4169 uint64_t Idx = Indices[i]->getZExtValue(); 4170 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4171 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4172 Init = cast<Constant>(CS->getOperand(Idx)); 4173 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4174 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4175 Init = cast<Constant>(CA->getOperand(Idx)); 4176 } else if (isa<ConstantAggregateZero>(Init)) { 4177 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 4178 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4179 Init = Constant::getNullValue(STy->getElementType(Idx)); 4180 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4181 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4182 Init = Constant::getNullValue(ATy->getElementType()); 4183 } else { 4184 llvm_unreachable("Unknown constant aggregate type!"); 4185 } 4186 return 0; 4187 } else { 4188 return 0; // Unknown initializer type 4189 } 4190 } 4191 return Init; 4192} 4193 4194/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 4195/// 'icmp op load X, cst', try to see if we can compute the backedge 4196/// execution count. 4197ScalarEvolution::BackedgeTakenInfo 4198ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 4199 LoadInst *LI, 4200 Constant *RHS, 4201 const Loop *L, 4202 ICmpInst::Predicate predicate) { 4203 if (LI->isVolatile()) return getCouldNotCompute(); 4204 4205 // Check to see if the loaded pointer is a getelementptr of a global. 4206 // TODO: Use SCEV instead of manually grubbing with GEPs. 4207 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4208 if (!GEP) return getCouldNotCompute(); 4209 4210 // Make sure that it is really a constant global we are gepping, with an 4211 // initializer, and make sure the first IDX is really 0. 4212 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4213 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4214 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4215 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4216 return getCouldNotCompute(); 4217 4218 // Okay, we allow one non-constant index into the GEP instruction. 4219 Value *VarIdx = 0; 4220 std::vector<ConstantInt*> Indexes; 4221 unsigned VarIdxNum = 0; 4222 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4223 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4224 Indexes.push_back(CI); 4225 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4226 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4227 VarIdx = GEP->getOperand(i); 4228 VarIdxNum = i-2; 4229 Indexes.push_back(0); 4230 } 4231 4232 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4233 // Check to see if X is a loop variant variable value now. 4234 const SCEV *Idx = getSCEV(VarIdx); 4235 Idx = getSCEVAtScope(Idx, L); 4236 4237 // We can only recognize very limited forms of loop index expressions, in 4238 // particular, only affine AddRec's like {C1,+,C2}. 4239 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4240 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) || 4241 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4242 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4243 return getCouldNotCompute(); 4244 4245 unsigned MaxSteps = MaxBruteForceIterations; 4246 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4247 ConstantInt *ItCst = ConstantInt::get( 4248 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4249 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4250 4251 // Form the GEP offset. 4252 Indexes[VarIdxNum] = Val; 4253 4254 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4255 if (Result == 0) break; // Cannot compute! 4256 4257 // Evaluate the condition for this iteration. 4258 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4259 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4260 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4261#if 0 4262 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4263 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4264 << "***\n"; 4265#endif 4266 ++NumArrayLenItCounts; 4267 return getConstant(ItCst); // Found terminating iteration! 4268 } 4269 } 4270 return getCouldNotCompute(); 4271} 4272 4273 4274/// CanConstantFold - Return true if we can constant fold an instruction of the 4275/// specified type, assuming that all operands were constants. 4276static bool CanConstantFold(const Instruction *I) { 4277 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4278 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4279 return true; 4280 4281 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4282 if (const Function *F = CI->getCalledFunction()) 4283 return canConstantFoldCallTo(F); 4284 return false; 4285} 4286 4287/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4288/// in the loop that V is derived from. We allow arbitrary operations along the 4289/// way, but the operands of an operation must either be constants or a value 4290/// derived from a constant PHI. If this expression does not fit with these 4291/// constraints, return null. 4292static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4293 // If this is not an instruction, or if this is an instruction outside of the 4294 // loop, it can't be derived from a loop PHI. 4295 Instruction *I = dyn_cast<Instruction>(V); 4296 if (I == 0 || !L->contains(I)) return 0; 4297 4298 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4299 if (L->getHeader() == I->getParent()) 4300 return PN; 4301 else 4302 // We don't currently keep track of the control flow needed to evaluate 4303 // PHIs, so we cannot handle PHIs inside of loops. 4304 return 0; 4305 } 4306 4307 // If we won't be able to constant fold this expression even if the operands 4308 // are constants, return early. 4309 if (!CanConstantFold(I)) return 0; 4310 4311 // Otherwise, we can evaluate this instruction if all of its operands are 4312 // constant or derived from a PHI node themselves. 4313 PHINode *PHI = 0; 4314 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4315 if (!isa<Constant>(I->getOperand(Op))) { 4316 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4317 if (P == 0) return 0; // Not evolving from PHI 4318 if (PHI == 0) 4319 PHI = P; 4320 else if (PHI != P) 4321 return 0; // Evolving from multiple different PHIs. 4322 } 4323 4324 // This is a expression evolving from a constant PHI! 4325 return PHI; 4326} 4327 4328/// EvaluateExpression - Given an expression that passes the 4329/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4330/// in the loop has the value PHIVal. If we can't fold this expression for some 4331/// reason, return null. 4332static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4333 const TargetData *TD) { 4334 if (isa<PHINode>(V)) return PHIVal; 4335 if (Constant *C = dyn_cast<Constant>(V)) return C; 4336 Instruction *I = cast<Instruction>(V); 4337 4338 std::vector<Constant*> Operands(I->getNumOperands()); 4339 4340 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4341 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4342 if (Operands[i] == 0) return 0; 4343 } 4344 4345 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4346 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4347 Operands[1], TD); 4348 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4349 &Operands[0], Operands.size(), TD); 4350} 4351 4352/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4353/// in the header of its containing loop, we know the loop executes a 4354/// constant number of times, and the PHI node is just a recurrence 4355/// involving constants, fold it. 4356Constant * 4357ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4358 const APInt &BEs, 4359 const Loop *L) { 4360 std::map<PHINode*, Constant*>::const_iterator I = 4361 ConstantEvolutionLoopExitValue.find(PN); 4362 if (I != ConstantEvolutionLoopExitValue.end()) 4363 return I->second; 4364 4365 if (BEs.ugt(MaxBruteForceIterations)) 4366 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4367 4368 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4369 4370 // Since the loop is canonicalized, the PHI node must have two entries. One 4371 // entry must be a constant (coming in from outside of the loop), and the 4372 // second must be derived from the same PHI. 4373 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4374 Constant *StartCST = 4375 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4376 if (StartCST == 0) 4377 return RetVal = 0; // Must be a constant. 4378 4379 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4380 if (getConstantEvolvingPHI(BEValue, L) != PN && 4381 !isa<Constant>(BEValue)) 4382 return RetVal = 0; // Not derived from same PHI. 4383 4384 // Execute the loop symbolically to determine the exit value. 4385 if (BEs.getActiveBits() >= 32) 4386 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4387 4388 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4389 unsigned IterationNum = 0; 4390 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4391 if (IterationNum == NumIterations) 4392 return RetVal = PHIVal; // Got exit value! 4393 4394 // Compute the value of the PHI node for the next iteration. 4395 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4396 if (NextPHI == PHIVal) 4397 return RetVal = NextPHI; // Stopped evolving! 4398 if (NextPHI == 0) 4399 return 0; // Couldn't evaluate! 4400 PHIVal = NextPHI; 4401 } 4402} 4403 4404/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4405/// constant number of times (the condition evolves only from constants), 4406/// try to evaluate a few iterations of the loop until we get the exit 4407/// condition gets a value of ExitWhen (true or false). If we cannot 4408/// evaluate the trip count of the loop, return getCouldNotCompute(). 4409const SCEV * 4410ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4411 Value *Cond, 4412 bool ExitWhen) { 4413 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4414 if (PN == 0) return getCouldNotCompute(); 4415 4416 // If the loop is canonicalized, the PHI will have exactly two entries. 4417 // That's the only form we support here. 4418 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4419 4420 // One entry must be a constant (coming in from outside of the loop), and the 4421 // second must be derived from the same PHI. 4422 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4423 Constant *StartCST = 4424 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4425 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4426 4427 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4428 if (getConstantEvolvingPHI(BEValue, L) != PN && 4429 !isa<Constant>(BEValue)) 4430 return getCouldNotCompute(); // Not derived from same PHI. 4431 4432 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4433 // the loop symbolically to determine when the condition gets a value of 4434 // "ExitWhen". 4435 unsigned IterationNum = 0; 4436 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4437 for (Constant *PHIVal = StartCST; 4438 IterationNum != MaxIterations; ++IterationNum) { 4439 ConstantInt *CondVal = 4440 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4441 4442 // Couldn't symbolically evaluate. 4443 if (!CondVal) return getCouldNotCompute(); 4444 4445 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4446 ++NumBruteForceTripCountsComputed; 4447 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4448 } 4449 4450 // Compute the value of the PHI node for the next iteration. 4451 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4452 if (NextPHI == 0 || NextPHI == PHIVal) 4453 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4454 PHIVal = NextPHI; 4455 } 4456 4457 // Too many iterations were needed to evaluate. 4458 return getCouldNotCompute(); 4459} 4460 4461/// getSCEVAtScope - Return a SCEV expression for the specified value 4462/// at the specified scope in the program. The L value specifies a loop 4463/// nest to evaluate the expression at, where null is the top-level or a 4464/// specified loop is immediately inside of the loop. 4465/// 4466/// This method can be used to compute the exit value for a variable defined 4467/// in a loop by querying what the value will hold in the parent loop. 4468/// 4469/// In the case that a relevant loop exit value cannot be computed, the 4470/// original value V is returned. 4471const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4472 // Check to see if we've folded this expression at this loop before. 4473 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4474 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4475 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4476 if (!Pair.second) 4477 return Pair.first->second ? Pair.first->second : V; 4478 4479 // Otherwise compute it. 4480 const SCEV *C = computeSCEVAtScope(V, L); 4481 ValuesAtScopes[V][L] = C; 4482 return C; 4483} 4484 4485const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4486 if (isa<SCEVConstant>(V)) return V; 4487 4488 // If this instruction is evolved from a constant-evolving PHI, compute the 4489 // exit value from the loop without using SCEVs. 4490 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4491 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4492 const Loop *LI = (*this->LI)[I->getParent()]; 4493 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4494 if (PHINode *PN = dyn_cast<PHINode>(I)) 4495 if (PN->getParent() == LI->getHeader()) { 4496 // Okay, there is no closed form solution for the PHI node. Check 4497 // to see if the loop that contains it has a known backedge-taken 4498 // count. If so, we may be able to force computation of the exit 4499 // value. 4500 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4501 if (const SCEVConstant *BTCC = 4502 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4503 // Okay, we know how many times the containing loop executes. If 4504 // this is a constant evolving PHI node, get the final value at 4505 // the specified iteration number. 4506 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4507 BTCC->getValue()->getValue(), 4508 LI); 4509 if (RV) return getSCEV(RV); 4510 } 4511 } 4512 4513 // Okay, this is an expression that we cannot symbolically evaluate 4514 // into a SCEV. Check to see if it's possible to symbolically evaluate 4515 // the arguments into constants, and if so, try to constant propagate the 4516 // result. This is particularly useful for computing loop exit values. 4517 if (CanConstantFold(I)) { 4518 SmallVector<Constant *, 4> Operands; 4519 bool MadeImprovement = false; 4520 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4521 Value *Op = I->getOperand(i); 4522 if (Constant *C = dyn_cast<Constant>(Op)) { 4523 Operands.push_back(C); 4524 continue; 4525 } 4526 4527 // If any of the operands is non-constant and if they are 4528 // non-integer and non-pointer, don't even try to analyze them 4529 // with scev techniques. 4530 if (!isSCEVable(Op->getType())) 4531 return V; 4532 4533 const SCEV *OrigV = getSCEV(Op); 4534 const SCEV *OpV = getSCEVAtScope(OrigV, L); 4535 MadeImprovement |= OrigV != OpV; 4536 4537 Constant *C = 0; 4538 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 4539 C = SC->getValue(); 4540 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) 4541 C = dyn_cast<Constant>(SU->getValue()); 4542 if (!C) return V; 4543 if (C->getType() != Op->getType()) 4544 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4545 Op->getType(), 4546 false), 4547 C, Op->getType()); 4548 Operands.push_back(C); 4549 } 4550 4551 // Check to see if getSCEVAtScope actually made an improvement. 4552 if (MadeImprovement) { 4553 Constant *C = 0; 4554 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4555 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4556 Operands[0], Operands[1], TD); 4557 else 4558 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4559 &Operands[0], Operands.size(), TD); 4560 if (!C) return V; 4561 return getSCEV(C); 4562 } 4563 } 4564 } 4565 4566 // This is some other type of SCEVUnknown, just return it. 4567 return V; 4568 } 4569 4570 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4571 // Avoid performing the look-up in the common case where the specified 4572 // expression has no loop-variant portions. 4573 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4574 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4575 if (OpAtScope != Comm->getOperand(i)) { 4576 // Okay, at least one of these operands is loop variant but might be 4577 // foldable. Build a new instance of the folded commutative expression. 4578 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4579 Comm->op_begin()+i); 4580 NewOps.push_back(OpAtScope); 4581 4582 for (++i; i != e; ++i) { 4583 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4584 NewOps.push_back(OpAtScope); 4585 } 4586 if (isa<SCEVAddExpr>(Comm)) 4587 return getAddExpr(NewOps); 4588 if (isa<SCEVMulExpr>(Comm)) 4589 return getMulExpr(NewOps); 4590 if (isa<SCEVSMaxExpr>(Comm)) 4591 return getSMaxExpr(NewOps); 4592 if (isa<SCEVUMaxExpr>(Comm)) 4593 return getUMaxExpr(NewOps); 4594 llvm_unreachable("Unknown commutative SCEV type!"); 4595 } 4596 } 4597 // If we got here, all operands are loop invariant. 4598 return Comm; 4599 } 4600 4601 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4602 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4603 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4604 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4605 return Div; // must be loop invariant 4606 return getUDivExpr(LHS, RHS); 4607 } 4608 4609 // If this is a loop recurrence for a loop that does not contain L, then we 4610 // are dealing with the final value computed by the loop. 4611 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4612 // First, attempt to evaluate each operand. 4613 // Avoid performing the look-up in the common case where the specified 4614 // expression has no loop-variant portions. 4615 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 4616 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 4617 if (OpAtScope == AddRec->getOperand(i)) 4618 continue; 4619 4620 // Okay, at least one of these operands is loop variant but might be 4621 // foldable. Build a new instance of the folded commutative expression. 4622 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 4623 AddRec->op_begin()+i); 4624 NewOps.push_back(OpAtScope); 4625 for (++i; i != e; ++i) 4626 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 4627 4628 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop())); 4629 break; 4630 } 4631 4632 // If the scope is outside the addrec's loop, evaluate it by using the 4633 // loop exit value of the addrec. 4634 if (!AddRec->getLoop()->contains(L)) { 4635 // To evaluate this recurrence, we need to know how many times the AddRec 4636 // loop iterates. Compute this now. 4637 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4638 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4639 4640 // Then, evaluate the AddRec. 4641 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4642 } 4643 4644 return AddRec; 4645 } 4646 4647 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4648 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4649 if (Op == Cast->getOperand()) 4650 return Cast; // must be loop invariant 4651 return getZeroExtendExpr(Op, Cast->getType()); 4652 } 4653 4654 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4655 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4656 if (Op == Cast->getOperand()) 4657 return Cast; // must be loop invariant 4658 return getSignExtendExpr(Op, Cast->getType()); 4659 } 4660 4661 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4662 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4663 if (Op == Cast->getOperand()) 4664 return Cast; // must be loop invariant 4665 return getTruncateExpr(Op, Cast->getType()); 4666 } 4667 4668 llvm_unreachable("Unknown SCEV type!"); 4669 return 0; 4670} 4671 4672/// getSCEVAtScope - This is a convenience function which does 4673/// getSCEVAtScope(getSCEV(V), L). 4674const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4675 return getSCEVAtScope(getSCEV(V), L); 4676} 4677 4678/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4679/// following equation: 4680/// 4681/// A * X = B (mod N) 4682/// 4683/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4684/// A and B isn't important. 4685/// 4686/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4687static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4688 ScalarEvolution &SE) { 4689 uint32_t BW = A.getBitWidth(); 4690 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4691 assert(A != 0 && "A must be non-zero."); 4692 4693 // 1. D = gcd(A, N) 4694 // 4695 // The gcd of A and N may have only one prime factor: 2. The number of 4696 // trailing zeros in A is its multiplicity 4697 uint32_t Mult2 = A.countTrailingZeros(); 4698 // D = 2^Mult2 4699 4700 // 2. Check if B is divisible by D. 4701 // 4702 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4703 // is not less than multiplicity of this prime factor for D. 4704 if (B.countTrailingZeros() < Mult2) 4705 return SE.getCouldNotCompute(); 4706 4707 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4708 // modulo (N / D). 4709 // 4710 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4711 // bit width during computations. 4712 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4713 APInt Mod(BW + 1, 0); 4714 Mod.setBit(BW - Mult2); // Mod = N / D 4715 APInt I = AD.multiplicativeInverse(Mod); 4716 4717 // 4. Compute the minimum unsigned root of the equation: 4718 // I * (B / D) mod (N / D) 4719 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4720 4721 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4722 // bits. 4723 return SE.getConstant(Result.trunc(BW)); 4724} 4725 4726/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4727/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4728/// might be the same) or two SCEVCouldNotCompute objects. 4729/// 4730static std::pair<const SCEV *,const SCEV *> 4731SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4732 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4733 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4734 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4735 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4736 4737 // We currently can only solve this if the coefficients are constants. 4738 if (!LC || !MC || !NC) { 4739 const SCEV *CNC = SE.getCouldNotCompute(); 4740 return std::make_pair(CNC, CNC); 4741 } 4742 4743 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4744 const APInt &L = LC->getValue()->getValue(); 4745 const APInt &M = MC->getValue()->getValue(); 4746 const APInt &N = NC->getValue()->getValue(); 4747 APInt Two(BitWidth, 2); 4748 APInt Four(BitWidth, 4); 4749 4750 { 4751 using namespace APIntOps; 4752 const APInt& C = L; 4753 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4754 // The B coefficient is M-N/2 4755 APInt B(M); 4756 B -= sdiv(N,Two); 4757 4758 // The A coefficient is N/2 4759 APInt A(N.sdiv(Two)); 4760 4761 // Compute the B^2-4ac term. 4762 APInt SqrtTerm(B); 4763 SqrtTerm *= B; 4764 SqrtTerm -= Four * (A * C); 4765 4766 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4767 // integer value or else APInt::sqrt() will assert. 4768 APInt SqrtVal(SqrtTerm.sqrt()); 4769 4770 // Compute the two solutions for the quadratic formula. 4771 // The divisions must be performed as signed divisions. 4772 APInt NegB(-B); 4773 APInt TwoA( A << 1 ); 4774 if (TwoA.isMinValue()) { 4775 const SCEV *CNC = SE.getCouldNotCompute(); 4776 return std::make_pair(CNC, CNC); 4777 } 4778 4779 LLVMContext &Context = SE.getContext(); 4780 4781 ConstantInt *Solution1 = 4782 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4783 ConstantInt *Solution2 = 4784 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4785 4786 return std::make_pair(SE.getConstant(Solution1), 4787 SE.getConstant(Solution2)); 4788 } // end APIntOps namespace 4789} 4790 4791/// HowFarToZero - Return the number of times a backedge comparing the specified 4792/// value to zero will execute. If not computable, return CouldNotCompute. 4793ScalarEvolution::BackedgeTakenInfo 4794ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4795 // If the value is a constant 4796 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4797 // If the value is already zero, the branch will execute zero times. 4798 if (C->getValue()->isZero()) return C; 4799 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4800 } 4801 4802 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4803 if (!AddRec || AddRec->getLoop() != L) 4804 return getCouldNotCompute(); 4805 4806 if (AddRec->isAffine()) { 4807 // If this is an affine expression, the execution count of this branch is 4808 // the minimum unsigned root of the following equation: 4809 // 4810 // Start + Step*N = 0 (mod 2^BW) 4811 // 4812 // equivalent to: 4813 // 4814 // Step*N = -Start (mod 2^BW) 4815 // 4816 // where BW is the common bit width of Start and Step. 4817 4818 // Get the initial value for the loop. 4819 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4820 L->getParentLoop()); 4821 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4822 L->getParentLoop()); 4823 4824 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4825 // For now we handle only constant steps. 4826 4827 // First, handle unitary steps. 4828 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4829 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4830 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4831 return Start; // N = Start (as unsigned) 4832 4833 // Then, try to solve the above equation provided that Start is constant. 4834 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4835 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4836 -StartC->getValue()->getValue(), 4837 *this); 4838 } 4839 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 4840 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4841 // the quadratic equation to solve it. 4842 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4843 *this); 4844 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4845 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4846 if (R1) { 4847#if 0 4848 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4849 << " sol#2: " << *R2 << "\n"; 4850#endif 4851 // Pick the smallest positive root value. 4852 if (ConstantInt *CB = 4853 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4854 R1->getValue(), R2->getValue()))) { 4855 if (CB->getZExtValue() == false) 4856 std::swap(R1, R2); // R1 is the minimum root now. 4857 4858 // We can only use this value if the chrec ends up with an exact zero 4859 // value at this index. When solving for "X*X != 5", for example, we 4860 // should not accept a root of 2. 4861 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4862 if (Val->isZero()) 4863 return R1; // We found a quadratic root! 4864 } 4865 } 4866 } 4867 4868 return getCouldNotCompute(); 4869} 4870 4871/// HowFarToNonZero - Return the number of times a backedge checking the 4872/// specified value for nonzero will execute. If not computable, return 4873/// CouldNotCompute 4874ScalarEvolution::BackedgeTakenInfo 4875ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4876 // Loops that look like: while (X == 0) are very strange indeed. We don't 4877 // handle them yet except for the trivial case. This could be expanded in the 4878 // future as needed. 4879 4880 // If the value is a constant, check to see if it is known to be non-zero 4881 // already. If so, the backedge will execute zero times. 4882 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4883 if (!C->getValue()->isNullValue()) 4884 return getConstant(C->getType(), 0); 4885 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4886 } 4887 4888 // We could implement others, but I really doubt anyone writes loops like 4889 // this, and if they did, they would already be constant folded. 4890 return getCouldNotCompute(); 4891} 4892 4893/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4894/// (which may not be an immediate predecessor) which has exactly one 4895/// successor from which BB is reachable, or null if no such block is 4896/// found. 4897/// 4898std::pair<BasicBlock *, BasicBlock *> 4899ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4900 // If the block has a unique predecessor, then there is no path from the 4901 // predecessor to the block that does not go through the direct edge 4902 // from the predecessor to the block. 4903 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4904 return std::make_pair(Pred, BB); 4905 4906 // A loop's header is defined to be a block that dominates the loop. 4907 // If the header has a unique predecessor outside the loop, it must be 4908 // a block that has exactly one successor that can reach the loop. 4909 if (Loop *L = LI->getLoopFor(BB)) 4910 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 4911 4912 return std::pair<BasicBlock *, BasicBlock *>(); 4913} 4914 4915/// HasSameValue - SCEV structural equivalence is usually sufficient for 4916/// testing whether two expressions are equal, however for the purposes of 4917/// looking for a condition guarding a loop, it can be useful to be a little 4918/// more general, since a front-end may have replicated the controlling 4919/// expression. 4920/// 4921static bool HasSameValue(const SCEV *A, const SCEV *B) { 4922 // Quick check to see if they are the same SCEV. 4923 if (A == B) return true; 4924 4925 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4926 // two different instructions with the same value. Check for this case. 4927 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4928 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4929 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4930 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4931 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4932 return true; 4933 4934 // Otherwise assume they may have a different value. 4935 return false; 4936} 4937 4938/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 4939/// predicate Pred. Return true iff any changes were made. 4940/// 4941bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 4942 const SCEV *&LHS, const SCEV *&RHS) { 4943 bool Changed = false; 4944 4945 // Canonicalize a constant to the right side. 4946 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 4947 // Check for both operands constant. 4948 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 4949 if (ConstantExpr::getICmp(Pred, 4950 LHSC->getValue(), 4951 RHSC->getValue())->isNullValue()) 4952 goto trivially_false; 4953 else 4954 goto trivially_true; 4955 } 4956 // Otherwise swap the operands to put the constant on the right. 4957 std::swap(LHS, RHS); 4958 Pred = ICmpInst::getSwappedPredicate(Pred); 4959 Changed = true; 4960 } 4961 4962 // If we're comparing an addrec with a value which is loop-invariant in the 4963 // addrec's loop, put the addrec on the left. Also make a dominance check, 4964 // as both operands could be addrecs loop-invariant in each other's loop. 4965 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 4966 const Loop *L = AR->getLoop(); 4967 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) { 4968 std::swap(LHS, RHS); 4969 Pred = ICmpInst::getSwappedPredicate(Pred); 4970 Changed = true; 4971 } 4972 } 4973 4974 // If there's a constant operand, canonicalize comparisons with boundary 4975 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 4976 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4977 const APInt &RA = RC->getValue()->getValue(); 4978 switch (Pred) { 4979 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4980 case ICmpInst::ICMP_EQ: 4981 case ICmpInst::ICMP_NE: 4982 break; 4983 case ICmpInst::ICMP_UGE: 4984 if ((RA - 1).isMinValue()) { 4985 Pred = ICmpInst::ICMP_NE; 4986 RHS = getConstant(RA - 1); 4987 Changed = true; 4988 break; 4989 } 4990 if (RA.isMaxValue()) { 4991 Pred = ICmpInst::ICMP_EQ; 4992 Changed = true; 4993 break; 4994 } 4995 if (RA.isMinValue()) goto trivially_true; 4996 4997 Pred = ICmpInst::ICMP_UGT; 4998 RHS = getConstant(RA - 1); 4999 Changed = true; 5000 break; 5001 case ICmpInst::ICMP_ULE: 5002 if ((RA + 1).isMaxValue()) { 5003 Pred = ICmpInst::ICMP_NE; 5004 RHS = getConstant(RA + 1); 5005 Changed = true; 5006 break; 5007 } 5008 if (RA.isMinValue()) { 5009 Pred = ICmpInst::ICMP_EQ; 5010 Changed = true; 5011 break; 5012 } 5013 if (RA.isMaxValue()) goto trivially_true; 5014 5015 Pred = ICmpInst::ICMP_ULT; 5016 RHS = getConstant(RA + 1); 5017 Changed = true; 5018 break; 5019 case ICmpInst::ICMP_SGE: 5020 if ((RA - 1).isMinSignedValue()) { 5021 Pred = ICmpInst::ICMP_NE; 5022 RHS = getConstant(RA - 1); 5023 Changed = true; 5024 break; 5025 } 5026 if (RA.isMaxSignedValue()) { 5027 Pred = ICmpInst::ICMP_EQ; 5028 Changed = true; 5029 break; 5030 } 5031 if (RA.isMinSignedValue()) goto trivially_true; 5032 5033 Pred = ICmpInst::ICMP_SGT; 5034 RHS = getConstant(RA - 1); 5035 Changed = true; 5036 break; 5037 case ICmpInst::ICMP_SLE: 5038 if ((RA + 1).isMaxSignedValue()) { 5039 Pred = ICmpInst::ICMP_NE; 5040 RHS = getConstant(RA + 1); 5041 Changed = true; 5042 break; 5043 } 5044 if (RA.isMinSignedValue()) { 5045 Pred = ICmpInst::ICMP_EQ; 5046 Changed = true; 5047 break; 5048 } 5049 if (RA.isMaxSignedValue()) goto trivially_true; 5050 5051 Pred = ICmpInst::ICMP_SLT; 5052 RHS = getConstant(RA + 1); 5053 Changed = true; 5054 break; 5055 case ICmpInst::ICMP_UGT: 5056 if (RA.isMinValue()) { 5057 Pred = ICmpInst::ICMP_NE; 5058 Changed = true; 5059 break; 5060 } 5061 if ((RA + 1).isMaxValue()) { 5062 Pred = ICmpInst::ICMP_EQ; 5063 RHS = getConstant(RA + 1); 5064 Changed = true; 5065 break; 5066 } 5067 if (RA.isMaxValue()) goto trivially_false; 5068 break; 5069 case ICmpInst::ICMP_ULT: 5070 if (RA.isMaxValue()) { 5071 Pred = ICmpInst::ICMP_NE; 5072 Changed = true; 5073 break; 5074 } 5075 if ((RA - 1).isMinValue()) { 5076 Pred = ICmpInst::ICMP_EQ; 5077 RHS = getConstant(RA - 1); 5078 Changed = true; 5079 break; 5080 } 5081 if (RA.isMinValue()) goto trivially_false; 5082 break; 5083 case ICmpInst::ICMP_SGT: 5084 if (RA.isMinSignedValue()) { 5085 Pred = ICmpInst::ICMP_NE; 5086 Changed = true; 5087 break; 5088 } 5089 if ((RA + 1).isMaxSignedValue()) { 5090 Pred = ICmpInst::ICMP_EQ; 5091 RHS = getConstant(RA + 1); 5092 Changed = true; 5093 break; 5094 } 5095 if (RA.isMaxSignedValue()) goto trivially_false; 5096 break; 5097 case ICmpInst::ICMP_SLT: 5098 if (RA.isMaxSignedValue()) { 5099 Pred = ICmpInst::ICMP_NE; 5100 Changed = true; 5101 break; 5102 } 5103 if ((RA - 1).isMinSignedValue()) { 5104 Pred = ICmpInst::ICMP_EQ; 5105 RHS = getConstant(RA - 1); 5106 Changed = true; 5107 break; 5108 } 5109 if (RA.isMinSignedValue()) goto trivially_false; 5110 break; 5111 } 5112 } 5113 5114 // Check for obvious equality. 5115 if (HasSameValue(LHS, RHS)) { 5116 if (ICmpInst::isTrueWhenEqual(Pred)) 5117 goto trivially_true; 5118 if (ICmpInst::isFalseWhenEqual(Pred)) 5119 goto trivially_false; 5120 } 5121 5122 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5123 // adding or subtracting 1 from one of the operands. 5124 switch (Pred) { 5125 case ICmpInst::ICMP_SLE: 5126 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5127 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5128 /*HasNUW=*/false, /*HasNSW=*/true); 5129 Pred = ICmpInst::ICMP_SLT; 5130 Changed = true; 5131 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5132 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5133 /*HasNUW=*/false, /*HasNSW=*/true); 5134 Pred = ICmpInst::ICMP_SLT; 5135 Changed = true; 5136 } 5137 break; 5138 case ICmpInst::ICMP_SGE: 5139 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5140 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5141 /*HasNUW=*/false, /*HasNSW=*/true); 5142 Pred = ICmpInst::ICMP_SGT; 5143 Changed = true; 5144 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5145 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5146 /*HasNUW=*/false, /*HasNSW=*/true); 5147 Pred = ICmpInst::ICMP_SGT; 5148 Changed = true; 5149 } 5150 break; 5151 case ICmpInst::ICMP_ULE: 5152 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5153 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5154 /*HasNUW=*/true, /*HasNSW=*/false); 5155 Pred = ICmpInst::ICMP_ULT; 5156 Changed = true; 5157 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5158 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5159 /*HasNUW=*/true, /*HasNSW=*/false); 5160 Pred = ICmpInst::ICMP_ULT; 5161 Changed = true; 5162 } 5163 break; 5164 case ICmpInst::ICMP_UGE: 5165 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5166 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5167 /*HasNUW=*/true, /*HasNSW=*/false); 5168 Pred = ICmpInst::ICMP_UGT; 5169 Changed = true; 5170 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5171 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5172 /*HasNUW=*/true, /*HasNSW=*/false); 5173 Pred = ICmpInst::ICMP_UGT; 5174 Changed = true; 5175 } 5176 break; 5177 default: 5178 break; 5179 } 5180 5181 // TODO: More simplifications are possible here. 5182 5183 return Changed; 5184 5185trivially_true: 5186 // Return 0 == 0. 5187 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5188 Pred = ICmpInst::ICMP_EQ; 5189 return true; 5190 5191trivially_false: 5192 // Return 0 != 0. 5193 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5194 Pred = ICmpInst::ICMP_NE; 5195 return true; 5196} 5197 5198bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5199 return getSignedRange(S).getSignedMax().isNegative(); 5200} 5201 5202bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5203 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5204} 5205 5206bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5207 return !getSignedRange(S).getSignedMin().isNegative(); 5208} 5209 5210bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5211 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5212} 5213 5214bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5215 return isKnownNegative(S) || isKnownPositive(S); 5216} 5217 5218bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5219 const SCEV *LHS, const SCEV *RHS) { 5220 // Canonicalize the inputs first. 5221 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5222 5223 // If LHS or RHS is an addrec, check to see if the condition is true in 5224 // every iteration of the loop. 5225 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5226 if (isLoopEntryGuardedByCond( 5227 AR->getLoop(), Pred, AR->getStart(), RHS) && 5228 isLoopBackedgeGuardedByCond( 5229 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5230 return true; 5231 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5232 if (isLoopEntryGuardedByCond( 5233 AR->getLoop(), Pred, LHS, AR->getStart()) && 5234 isLoopBackedgeGuardedByCond( 5235 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5236 return true; 5237 5238 // Otherwise see what can be done with known constant ranges. 5239 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5240} 5241 5242bool 5243ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5244 const SCEV *LHS, const SCEV *RHS) { 5245 if (HasSameValue(LHS, RHS)) 5246 return ICmpInst::isTrueWhenEqual(Pred); 5247 5248 // This code is split out from isKnownPredicate because it is called from 5249 // within isLoopEntryGuardedByCond. 5250 switch (Pred) { 5251 default: 5252 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5253 break; 5254 case ICmpInst::ICMP_SGT: 5255 Pred = ICmpInst::ICMP_SLT; 5256 std::swap(LHS, RHS); 5257 case ICmpInst::ICMP_SLT: { 5258 ConstantRange LHSRange = getSignedRange(LHS); 5259 ConstantRange RHSRange = getSignedRange(RHS); 5260 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5261 return true; 5262 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5263 return false; 5264 break; 5265 } 5266 case ICmpInst::ICMP_SGE: 5267 Pred = ICmpInst::ICMP_SLE; 5268 std::swap(LHS, RHS); 5269 case ICmpInst::ICMP_SLE: { 5270 ConstantRange LHSRange = getSignedRange(LHS); 5271 ConstantRange RHSRange = getSignedRange(RHS); 5272 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5273 return true; 5274 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5275 return false; 5276 break; 5277 } 5278 case ICmpInst::ICMP_UGT: 5279 Pred = ICmpInst::ICMP_ULT; 5280 std::swap(LHS, RHS); 5281 case ICmpInst::ICMP_ULT: { 5282 ConstantRange LHSRange = getUnsignedRange(LHS); 5283 ConstantRange RHSRange = getUnsignedRange(RHS); 5284 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5285 return true; 5286 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5287 return false; 5288 break; 5289 } 5290 case ICmpInst::ICMP_UGE: 5291 Pred = ICmpInst::ICMP_ULE; 5292 std::swap(LHS, RHS); 5293 case ICmpInst::ICMP_ULE: { 5294 ConstantRange LHSRange = getUnsignedRange(LHS); 5295 ConstantRange RHSRange = getUnsignedRange(RHS); 5296 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5297 return true; 5298 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5299 return false; 5300 break; 5301 } 5302 case ICmpInst::ICMP_NE: { 5303 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5304 return true; 5305 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5306 return true; 5307 5308 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5309 if (isKnownNonZero(Diff)) 5310 return true; 5311 break; 5312 } 5313 case ICmpInst::ICMP_EQ: 5314 // The check at the top of the function catches the case where 5315 // the values are known to be equal. 5316 break; 5317 } 5318 return false; 5319} 5320 5321/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5322/// protected by a conditional between LHS and RHS. This is used to 5323/// to eliminate casts. 5324bool 5325ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5326 ICmpInst::Predicate Pred, 5327 const SCEV *LHS, const SCEV *RHS) { 5328 // Interpret a null as meaning no loop, where there is obviously no guard 5329 // (interprocedural conditions notwithstanding). 5330 if (!L) return true; 5331 5332 BasicBlock *Latch = L->getLoopLatch(); 5333 if (!Latch) 5334 return false; 5335 5336 BranchInst *LoopContinuePredicate = 5337 dyn_cast<BranchInst>(Latch->getTerminator()); 5338 if (!LoopContinuePredicate || 5339 LoopContinuePredicate->isUnconditional()) 5340 return false; 5341 5342 return isImpliedCond(Pred, LHS, RHS, 5343 LoopContinuePredicate->getCondition(), 5344 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5345} 5346 5347/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5348/// by a conditional between LHS and RHS. This is used to help avoid max 5349/// expressions in loop trip counts, and to eliminate casts. 5350bool 5351ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5352 ICmpInst::Predicate Pred, 5353 const SCEV *LHS, const SCEV *RHS) { 5354 // Interpret a null as meaning no loop, where there is obviously no guard 5355 // (interprocedural conditions notwithstanding). 5356 if (!L) return false; 5357 5358 // Starting at the loop predecessor, climb up the predecessor chain, as long 5359 // as there are predecessors that can be found that have unique successors 5360 // leading to the original header. 5361 for (std::pair<BasicBlock *, BasicBlock *> 5362 Pair(L->getLoopPredecessor(), L->getHeader()); 5363 Pair.first; 5364 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5365 5366 BranchInst *LoopEntryPredicate = 5367 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5368 if (!LoopEntryPredicate || 5369 LoopEntryPredicate->isUnconditional()) 5370 continue; 5371 5372 if (isImpliedCond(Pred, LHS, RHS, 5373 LoopEntryPredicate->getCondition(), 5374 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5375 return true; 5376 } 5377 5378 return false; 5379} 5380 5381/// isImpliedCond - Test whether the condition described by Pred, LHS, 5382/// and RHS is true whenever the given Cond value evaluates to true. 5383bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 5384 const SCEV *LHS, const SCEV *RHS, 5385 Value *FoundCondValue, 5386 bool Inverse) { 5387 // Recursively handle And and Or conditions. 5388 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 5389 if (BO->getOpcode() == Instruction::And) { 5390 if (!Inverse) 5391 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5392 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5393 } else if (BO->getOpcode() == Instruction::Or) { 5394 if (Inverse) 5395 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5396 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5397 } 5398 } 5399 5400 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 5401 if (!ICI) return false; 5402 5403 // Bail if the ICmp's operands' types are wider than the needed type 5404 // before attempting to call getSCEV on them. This avoids infinite 5405 // recursion, since the analysis of widening casts can require loop 5406 // exit condition information for overflow checking, which would 5407 // lead back here. 5408 if (getTypeSizeInBits(LHS->getType()) < 5409 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5410 return false; 5411 5412 // Now that we found a conditional branch that dominates the loop, check to 5413 // see if it is the comparison we are looking for. 5414 ICmpInst::Predicate FoundPred; 5415 if (Inverse) 5416 FoundPred = ICI->getInversePredicate(); 5417 else 5418 FoundPred = ICI->getPredicate(); 5419 5420 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5421 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5422 5423 // Balance the types. The case where FoundLHS' type is wider than 5424 // LHS' type is checked for above. 5425 if (getTypeSizeInBits(LHS->getType()) > 5426 getTypeSizeInBits(FoundLHS->getType())) { 5427 if (CmpInst::isSigned(Pred)) { 5428 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5429 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5430 } else { 5431 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5432 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5433 } 5434 } 5435 5436 // Canonicalize the query to match the way instcombine will have 5437 // canonicalized the comparison. 5438 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5439 if (LHS == RHS) 5440 return CmpInst::isTrueWhenEqual(Pred); 5441 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5442 if (FoundLHS == FoundRHS) 5443 return CmpInst::isFalseWhenEqual(Pred); 5444 5445 // Check to see if we can make the LHS or RHS match. 5446 if (LHS == FoundRHS || RHS == FoundLHS) { 5447 if (isa<SCEVConstant>(RHS)) { 5448 std::swap(FoundLHS, FoundRHS); 5449 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5450 } else { 5451 std::swap(LHS, RHS); 5452 Pred = ICmpInst::getSwappedPredicate(Pred); 5453 } 5454 } 5455 5456 // Check whether the found predicate is the same as the desired predicate. 5457 if (FoundPred == Pred) 5458 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5459 5460 // Check whether swapping the found predicate makes it the same as the 5461 // desired predicate. 5462 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5463 if (isa<SCEVConstant>(RHS)) 5464 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5465 else 5466 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5467 RHS, LHS, FoundLHS, FoundRHS); 5468 } 5469 5470 // Check whether the actual condition is beyond sufficient. 5471 if (FoundPred == ICmpInst::ICMP_EQ) 5472 if (ICmpInst::isTrueWhenEqual(Pred)) 5473 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5474 return true; 5475 if (Pred == ICmpInst::ICMP_NE) 5476 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5477 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5478 return true; 5479 5480 // Otherwise assume the worst. 5481 return false; 5482} 5483 5484/// isImpliedCondOperands - Test whether the condition described by Pred, 5485/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5486/// and FoundRHS is true. 5487bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5488 const SCEV *LHS, const SCEV *RHS, 5489 const SCEV *FoundLHS, 5490 const SCEV *FoundRHS) { 5491 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5492 FoundLHS, FoundRHS) || 5493 // ~x < ~y --> x > y 5494 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5495 getNotSCEV(FoundRHS), 5496 getNotSCEV(FoundLHS)); 5497} 5498 5499/// isImpliedCondOperandsHelper - Test whether the condition described by 5500/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5501/// FoundLHS, and FoundRHS is true. 5502bool 5503ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5504 const SCEV *LHS, const SCEV *RHS, 5505 const SCEV *FoundLHS, 5506 const SCEV *FoundRHS) { 5507 switch (Pred) { 5508 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5509 case ICmpInst::ICMP_EQ: 5510 case ICmpInst::ICMP_NE: 5511 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5512 return true; 5513 break; 5514 case ICmpInst::ICMP_SLT: 5515 case ICmpInst::ICMP_SLE: 5516 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5517 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5518 return true; 5519 break; 5520 case ICmpInst::ICMP_SGT: 5521 case ICmpInst::ICMP_SGE: 5522 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5523 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5524 return true; 5525 break; 5526 case ICmpInst::ICMP_ULT: 5527 case ICmpInst::ICMP_ULE: 5528 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5529 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5530 return true; 5531 break; 5532 case ICmpInst::ICMP_UGT: 5533 case ICmpInst::ICMP_UGE: 5534 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5535 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5536 return true; 5537 break; 5538 } 5539 5540 return false; 5541} 5542 5543/// getBECount - Subtract the end and start values and divide by the step, 5544/// rounding up, to get the number of times the backedge is executed. Return 5545/// CouldNotCompute if an intermediate computation overflows. 5546const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5547 const SCEV *End, 5548 const SCEV *Step, 5549 bool NoWrap) { 5550 assert(!isKnownNegative(Step) && 5551 "This code doesn't handle negative strides yet!"); 5552 5553 const Type *Ty = Start->getType(); 5554 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5555 const SCEV *Diff = getMinusSCEV(End, Start); 5556 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5557 5558 // Add an adjustment to the difference between End and Start so that 5559 // the division will effectively round up. 5560 const SCEV *Add = getAddExpr(Diff, RoundUp); 5561 5562 if (!NoWrap) { 5563 // Check Add for unsigned overflow. 5564 // TODO: More sophisticated things could be done here. 5565 const Type *WideTy = IntegerType::get(getContext(), 5566 getTypeSizeInBits(Ty) + 1); 5567 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5568 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5569 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5570 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5571 return getCouldNotCompute(); 5572 } 5573 5574 return getUDivExpr(Add, Step); 5575} 5576 5577/// HowManyLessThans - Return the number of times a backedge containing the 5578/// specified less-than comparison will execute. If not computable, return 5579/// CouldNotCompute. 5580ScalarEvolution::BackedgeTakenInfo 5581ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5582 const Loop *L, bool isSigned) { 5583 // Only handle: "ADDREC < LoopInvariant". 5584 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute(); 5585 5586 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5587 if (!AddRec || AddRec->getLoop() != L) 5588 return getCouldNotCompute(); 5589 5590 // Check to see if we have a flag which makes analysis easy. 5591 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5592 AddRec->hasNoUnsignedWrap(); 5593 5594 if (AddRec->isAffine()) { 5595 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5596 const SCEV *Step = AddRec->getStepRecurrence(*this); 5597 5598 if (Step->isZero()) 5599 return getCouldNotCompute(); 5600 if (Step->isOne()) { 5601 // With unit stride, the iteration never steps past the limit value. 5602 } else if (isKnownPositive(Step)) { 5603 // Test whether a positive iteration can step past the limit 5604 // value and past the maximum value for its type in a single step. 5605 // Note that it's not sufficient to check NoWrap here, because even 5606 // though the value after a wrap is undefined, it's not undefined 5607 // behavior, so if wrap does occur, the loop could either terminate or 5608 // loop infinitely, but in either case, the loop is guaranteed to 5609 // iterate at least until the iteration where the wrapping occurs. 5610 const SCEV *One = getConstant(Step->getType(), 1); 5611 if (isSigned) { 5612 APInt Max = APInt::getSignedMaxValue(BitWidth); 5613 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5614 .slt(getSignedRange(RHS).getSignedMax())) 5615 return getCouldNotCompute(); 5616 } else { 5617 APInt Max = APInt::getMaxValue(BitWidth); 5618 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5619 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5620 return getCouldNotCompute(); 5621 } 5622 } else 5623 // TODO: Handle negative strides here and below. 5624 return getCouldNotCompute(); 5625 5626 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5627 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5628 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5629 // treat m-n as signed nor unsigned due to overflow possibility. 5630 5631 // First, we get the value of the LHS in the first iteration: n 5632 const SCEV *Start = AddRec->getOperand(0); 5633 5634 // Determine the minimum constant start value. 5635 const SCEV *MinStart = getConstant(isSigned ? 5636 getSignedRange(Start).getSignedMin() : 5637 getUnsignedRange(Start).getUnsignedMin()); 5638 5639 // If we know that the condition is true in order to enter the loop, 5640 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5641 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5642 // the division must round up. 5643 const SCEV *End = RHS; 5644 if (!isLoopEntryGuardedByCond(L, 5645 isSigned ? ICmpInst::ICMP_SLT : 5646 ICmpInst::ICMP_ULT, 5647 getMinusSCEV(Start, Step), RHS)) 5648 End = isSigned ? getSMaxExpr(RHS, Start) 5649 : getUMaxExpr(RHS, Start); 5650 5651 // Determine the maximum constant end value. 5652 const SCEV *MaxEnd = getConstant(isSigned ? 5653 getSignedRange(End).getSignedMax() : 5654 getUnsignedRange(End).getUnsignedMax()); 5655 5656 // If MaxEnd is within a step of the maximum integer value in its type, 5657 // adjust it down to the minimum value which would produce the same effect. 5658 // This allows the subsequent ceiling division of (N+(step-1))/step to 5659 // compute the correct value. 5660 const SCEV *StepMinusOne = getMinusSCEV(Step, 5661 getConstant(Step->getType(), 1)); 5662 MaxEnd = isSigned ? 5663 getSMinExpr(MaxEnd, 5664 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5665 StepMinusOne)) : 5666 getUMinExpr(MaxEnd, 5667 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5668 StepMinusOne)); 5669 5670 // Finally, we subtract these two values and divide, rounding up, to get 5671 // the number of times the backedge is executed. 5672 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5673 5674 // The maximum backedge count is similar, except using the minimum start 5675 // value and the maximum end value. 5676 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5677 5678 return BackedgeTakenInfo(BECount, MaxBECount); 5679 } 5680 5681 return getCouldNotCompute(); 5682} 5683 5684/// getNumIterationsInRange - Return the number of iterations of this loop that 5685/// produce values in the specified constant range. Another way of looking at 5686/// this is that it returns the first iteration number where the value is not in 5687/// the condition, thus computing the exit count. If the iteration count can't 5688/// be computed, an instance of SCEVCouldNotCompute is returned. 5689const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5690 ScalarEvolution &SE) const { 5691 if (Range.isFullSet()) // Infinite loop. 5692 return SE.getCouldNotCompute(); 5693 5694 // If the start is a non-zero constant, shift the range to simplify things. 5695 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5696 if (!SC->getValue()->isZero()) { 5697 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5698 Operands[0] = SE.getConstant(SC->getType(), 0); 5699 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5700 if (const SCEVAddRecExpr *ShiftedAddRec = 5701 dyn_cast<SCEVAddRecExpr>(Shifted)) 5702 return ShiftedAddRec->getNumIterationsInRange( 5703 Range.subtract(SC->getValue()->getValue()), SE); 5704 // This is strange and shouldn't happen. 5705 return SE.getCouldNotCompute(); 5706 } 5707 5708 // The only time we can solve this is when we have all constant indices. 5709 // Otherwise, we cannot determine the overflow conditions. 5710 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5711 if (!isa<SCEVConstant>(getOperand(i))) 5712 return SE.getCouldNotCompute(); 5713 5714 5715 // Okay at this point we know that all elements of the chrec are constants and 5716 // that the start element is zero. 5717 5718 // First check to see if the range contains zero. If not, the first 5719 // iteration exits. 5720 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5721 if (!Range.contains(APInt(BitWidth, 0))) 5722 return SE.getConstant(getType(), 0); 5723 5724 if (isAffine()) { 5725 // If this is an affine expression then we have this situation: 5726 // Solve {0,+,A} in Range === Ax in Range 5727 5728 // We know that zero is in the range. If A is positive then we know that 5729 // the upper value of the range must be the first possible exit value. 5730 // If A is negative then the lower of the range is the last possible loop 5731 // value. Also note that we already checked for a full range. 5732 APInt One(BitWidth,1); 5733 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5734 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5735 5736 // The exit value should be (End+A)/A. 5737 APInt ExitVal = (End + A).udiv(A); 5738 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5739 5740 // Evaluate at the exit value. If we really did fall out of the valid 5741 // range, then we computed our trip count, otherwise wrap around or other 5742 // things must have happened. 5743 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5744 if (Range.contains(Val->getValue())) 5745 return SE.getCouldNotCompute(); // Something strange happened 5746 5747 // Ensure that the previous value is in the range. This is a sanity check. 5748 assert(Range.contains( 5749 EvaluateConstantChrecAtConstant(this, 5750 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5751 "Linear scev computation is off in a bad way!"); 5752 return SE.getConstant(ExitValue); 5753 } else if (isQuadratic()) { 5754 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5755 // quadratic equation to solve it. To do this, we must frame our problem in 5756 // terms of figuring out when zero is crossed, instead of when 5757 // Range.getUpper() is crossed. 5758 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5759 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5760 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5761 5762 // Next, solve the constructed addrec 5763 std::pair<const SCEV *,const SCEV *> Roots = 5764 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5765 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5766 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5767 if (R1) { 5768 // Pick the smallest positive root value. 5769 if (ConstantInt *CB = 5770 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5771 R1->getValue(), R2->getValue()))) { 5772 if (CB->getZExtValue() == false) 5773 std::swap(R1, R2); // R1 is the minimum root now. 5774 5775 // Make sure the root is not off by one. The returned iteration should 5776 // not be in the range, but the previous one should be. When solving 5777 // for "X*X < 5", for example, we should not return a root of 2. 5778 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5779 R1->getValue(), 5780 SE); 5781 if (Range.contains(R1Val->getValue())) { 5782 // The next iteration must be out of the range... 5783 ConstantInt *NextVal = 5784 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5785 5786 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5787 if (!Range.contains(R1Val->getValue())) 5788 return SE.getConstant(NextVal); 5789 return SE.getCouldNotCompute(); // Something strange happened 5790 } 5791 5792 // If R1 was not in the range, then it is a good return value. Make 5793 // sure that R1-1 WAS in the range though, just in case. 5794 ConstantInt *NextVal = 5795 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5796 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5797 if (Range.contains(R1Val->getValue())) 5798 return R1; 5799 return SE.getCouldNotCompute(); // Something strange happened 5800 } 5801 } 5802 } 5803 5804 return SE.getCouldNotCompute(); 5805} 5806 5807 5808 5809//===----------------------------------------------------------------------===// 5810// SCEVCallbackVH Class Implementation 5811//===----------------------------------------------------------------------===// 5812 5813void ScalarEvolution::SCEVCallbackVH::deleted() { 5814 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5815 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5816 SE->ConstantEvolutionLoopExitValue.erase(PN); 5817 SE->ValueExprMap.erase(getValPtr()); 5818 // this now dangles! 5819} 5820 5821void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 5822 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5823 5824 // Forget all the expressions associated with users of the old value, 5825 // so that future queries will recompute the expressions using the new 5826 // value. 5827 Value *Old = getValPtr(); 5828 SmallVector<User *, 16> Worklist; 5829 SmallPtrSet<User *, 8> Visited; 5830 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5831 UI != UE; ++UI) 5832 Worklist.push_back(*UI); 5833 while (!Worklist.empty()) { 5834 User *U = Worklist.pop_back_val(); 5835 // Deleting the Old value will cause this to dangle. Postpone 5836 // that until everything else is done. 5837 if (U == Old) 5838 continue; 5839 if (!Visited.insert(U)) 5840 continue; 5841 if (PHINode *PN = dyn_cast<PHINode>(U)) 5842 SE->ConstantEvolutionLoopExitValue.erase(PN); 5843 SE->ValueExprMap.erase(U); 5844 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5845 UI != UE; ++UI) 5846 Worklist.push_back(*UI); 5847 } 5848 // Delete the Old value. 5849 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5850 SE->ConstantEvolutionLoopExitValue.erase(PN); 5851 SE->ValueExprMap.erase(Old); 5852 // this now dangles! 5853} 5854 5855ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5856 : CallbackVH(V), SE(se) {} 5857 5858//===----------------------------------------------------------------------===// 5859// ScalarEvolution Class Implementation 5860//===----------------------------------------------------------------------===// 5861 5862ScalarEvolution::ScalarEvolution() 5863 : FunctionPass(ID), FirstUnknown(0) { 5864 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry()); 5865} 5866 5867bool ScalarEvolution::runOnFunction(Function &F) { 5868 this->F = &F; 5869 LI = &getAnalysis<LoopInfo>(); 5870 TD = getAnalysisIfAvailable<TargetData>(); 5871 DT = &getAnalysis<DominatorTree>(); 5872 return false; 5873} 5874 5875void ScalarEvolution::releaseMemory() { 5876 // Iterate through all the SCEVUnknown instances and call their 5877 // destructors, so that they release their references to their values. 5878 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 5879 U->~SCEVUnknown(); 5880 FirstUnknown = 0; 5881 5882 ValueExprMap.clear(); 5883 BackedgeTakenCounts.clear(); 5884 ConstantEvolutionLoopExitValue.clear(); 5885 ValuesAtScopes.clear(); 5886 LoopDispositions.clear(); 5887 BlockDispositions.clear(); 5888 UnsignedRanges.clear(); 5889 SignedRanges.clear(); 5890 UniqueSCEVs.clear(); 5891 SCEVAllocator.Reset(); 5892} 5893 5894void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5895 AU.setPreservesAll(); 5896 AU.addRequiredTransitive<LoopInfo>(); 5897 AU.addRequiredTransitive<DominatorTree>(); 5898} 5899 5900bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5901 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5902} 5903 5904static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5905 const Loop *L) { 5906 // Print all inner loops first 5907 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5908 PrintLoopInfo(OS, SE, *I); 5909 5910 OS << "Loop "; 5911 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5912 OS << ": "; 5913 5914 SmallVector<BasicBlock *, 8> ExitBlocks; 5915 L->getExitBlocks(ExitBlocks); 5916 if (ExitBlocks.size() != 1) 5917 OS << "<multiple exits> "; 5918 5919 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5920 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5921 } else { 5922 OS << "Unpredictable backedge-taken count. "; 5923 } 5924 5925 OS << "\n" 5926 "Loop "; 5927 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5928 OS << ": "; 5929 5930 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5931 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5932 } else { 5933 OS << "Unpredictable max backedge-taken count. "; 5934 } 5935 5936 OS << "\n"; 5937} 5938 5939void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 5940 // ScalarEvolution's implementation of the print method is to print 5941 // out SCEV values of all instructions that are interesting. Doing 5942 // this potentially causes it to create new SCEV objects though, 5943 // which technically conflicts with the const qualifier. This isn't 5944 // observable from outside the class though, so casting away the 5945 // const isn't dangerous. 5946 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 5947 5948 OS << "Classifying expressions for: "; 5949 WriteAsOperand(OS, F, /*PrintType=*/false); 5950 OS << "\n"; 5951 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5952 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 5953 OS << *I << '\n'; 5954 OS << " --> "; 5955 const SCEV *SV = SE.getSCEV(&*I); 5956 SV->print(OS); 5957 5958 const Loop *L = LI->getLoopFor((*I).getParent()); 5959 5960 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5961 if (AtUse != SV) { 5962 OS << " --> "; 5963 AtUse->print(OS); 5964 } 5965 5966 if (L) { 5967 OS << "\t\t" "Exits: "; 5968 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5969 if (!SE.isLoopInvariant(ExitValue, L)) { 5970 OS << "<<Unknown>>"; 5971 } else { 5972 OS << *ExitValue; 5973 } 5974 } 5975 5976 OS << "\n"; 5977 } 5978 5979 OS << "Determining loop execution counts for: "; 5980 WriteAsOperand(OS, F, /*PrintType=*/false); 5981 OS << "\n"; 5982 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5983 PrintLoopInfo(OS, &SE, *I); 5984} 5985 5986ScalarEvolution::LoopDisposition 5987ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) { 5988 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S]; 5989 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair = 5990 Values.insert(std::make_pair(L, LoopVariant)); 5991 if (!Pair.second) 5992 return Pair.first->second; 5993 5994 LoopDisposition D = computeLoopDisposition(S, L); 5995 return LoopDispositions[S][L] = D; 5996} 5997 5998ScalarEvolution::LoopDisposition 5999ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) { 6000 switch (S->getSCEVType()) { 6001 case scConstant: 6002 return LoopInvariant; 6003 case scTruncate: 6004 case scZeroExtend: 6005 case scSignExtend: 6006 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L); 6007 case scAddRecExpr: { 6008 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6009 6010 // If L is the addrec's loop, it's computable. 6011 if (AR->getLoop() == L) 6012 return LoopComputable; 6013 6014 // Add recurrences are never invariant in the function-body (null loop). 6015 if (!L) 6016 return LoopVariant; 6017 6018 // This recurrence is variant w.r.t. L if L contains AR's loop. 6019 if (L->contains(AR->getLoop())) 6020 return LoopVariant; 6021 6022 // This recurrence is invariant w.r.t. L if AR's loop contains L. 6023 if (AR->getLoop()->contains(L)) 6024 return LoopInvariant; 6025 6026 // This recurrence is variant w.r.t. L if any of its operands 6027 // are variant. 6028 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 6029 I != E; ++I) 6030 if (!isLoopInvariant(*I, L)) 6031 return LoopVariant; 6032 6033 // Otherwise it's loop-invariant. 6034 return LoopInvariant; 6035 } 6036 case scAddExpr: 6037 case scMulExpr: 6038 case scUMaxExpr: 6039 case scSMaxExpr: { 6040 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6041 bool HasVarying = false; 6042 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6043 I != E; ++I) { 6044 LoopDisposition D = getLoopDisposition(*I, L); 6045 if (D == LoopVariant) 6046 return LoopVariant; 6047 if (D == LoopComputable) 6048 HasVarying = true; 6049 } 6050 return HasVarying ? LoopComputable : LoopInvariant; 6051 } 6052 case scUDivExpr: { 6053 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6054 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L); 6055 if (LD == LoopVariant) 6056 return LoopVariant; 6057 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L); 6058 if (RD == LoopVariant) 6059 return LoopVariant; 6060 return (LD == LoopInvariant && RD == LoopInvariant) ? 6061 LoopInvariant : LoopComputable; 6062 } 6063 case scUnknown: 6064 // All non-instruction values are loop invariant. All instructions are loop 6065 // invariant if they are not contained in the specified loop. 6066 // Instructions are never considered invariant in the function body 6067 // (null loop) because they are defined within the "loop". 6068 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) 6069 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; 6070 return LoopInvariant; 6071 case scCouldNotCompute: 6072 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6073 return LoopVariant; 6074 default: break; 6075 } 6076 llvm_unreachable("Unknown SCEV kind!"); 6077 return LoopVariant; 6078} 6079 6080bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { 6081 return getLoopDisposition(S, L) == LoopInvariant; 6082} 6083 6084bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { 6085 return getLoopDisposition(S, L) == LoopComputable; 6086} 6087 6088ScalarEvolution::BlockDisposition 6089ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6090 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S]; 6091 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool> 6092 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock)); 6093 if (!Pair.second) 6094 return Pair.first->second; 6095 6096 BlockDisposition D = computeBlockDisposition(S, BB); 6097 return BlockDispositions[S][BB] = D; 6098} 6099 6100ScalarEvolution::BlockDisposition 6101ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6102 switch (S->getSCEVType()) { 6103 case scConstant: 6104 return ProperlyDominatesBlock; 6105 case scTruncate: 6106 case scZeroExtend: 6107 case scSignExtend: 6108 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB); 6109 case scAddRecExpr: { 6110 // This uses a "dominates" query instead of "properly dominates" query 6111 // to test for proper dominance too, because the instruction which 6112 // produces the addrec's value is a PHI, and a PHI effectively properly 6113 // dominates its entire containing block. 6114 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6115 if (!DT->dominates(AR->getLoop()->getHeader(), BB)) 6116 return DoesNotDominateBlock; 6117 } 6118 // FALL THROUGH into SCEVNAryExpr handling. 6119 case scAddExpr: 6120 case scMulExpr: 6121 case scUMaxExpr: 6122 case scSMaxExpr: { 6123 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6124 bool Proper = true; 6125 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6126 I != E; ++I) { 6127 BlockDisposition D = getBlockDisposition(*I, BB); 6128 if (D == DoesNotDominateBlock) 6129 return DoesNotDominateBlock; 6130 if (D == DominatesBlock) 6131 Proper = false; 6132 } 6133 return Proper ? ProperlyDominatesBlock : DominatesBlock; 6134 } 6135 case scUDivExpr: { 6136 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6137 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6138 BlockDisposition LD = getBlockDisposition(LHS, BB); 6139 if (LD == DoesNotDominateBlock) 6140 return DoesNotDominateBlock; 6141 BlockDisposition RD = getBlockDisposition(RHS, BB); 6142 if (RD == DoesNotDominateBlock) 6143 return DoesNotDominateBlock; 6144 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ? 6145 ProperlyDominatesBlock : DominatesBlock; 6146 } 6147 case scUnknown: 6148 if (Instruction *I = 6149 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) { 6150 if (I->getParent() == BB) 6151 return DominatesBlock; 6152 if (DT->properlyDominates(I->getParent(), BB)) 6153 return ProperlyDominatesBlock; 6154 return DoesNotDominateBlock; 6155 } 6156 return ProperlyDominatesBlock; 6157 case scCouldNotCompute: 6158 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6159 return DoesNotDominateBlock; 6160 default: break; 6161 } 6162 llvm_unreachable("Unknown SCEV kind!"); 6163 return DoesNotDominateBlock; 6164} 6165 6166bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) { 6167 return getBlockDisposition(S, BB) >= DominatesBlock; 6168} 6169 6170bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) { 6171 return getBlockDisposition(S, BB) == ProperlyDominatesBlock; 6172} 6173 6174bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { 6175 switch (S->getSCEVType()) { 6176 case scConstant: 6177 return false; 6178 case scTruncate: 6179 case scZeroExtend: 6180 case scSignExtend: { 6181 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S); 6182 const SCEV *CastOp = Cast->getOperand(); 6183 return Op == CastOp || hasOperand(CastOp, Op); 6184 } 6185 case scAddRecExpr: 6186 case scAddExpr: 6187 case scMulExpr: 6188 case scUMaxExpr: 6189 case scSMaxExpr: { 6190 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6191 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6192 I != E; ++I) { 6193 const SCEV *NAryOp = *I; 6194 if (NAryOp == Op || hasOperand(NAryOp, Op)) 6195 return true; 6196 } 6197 return false; 6198 } 6199 case scUDivExpr: { 6200 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6201 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6202 return LHS == Op || hasOperand(LHS, Op) || 6203 RHS == Op || hasOperand(RHS, Op); 6204 } 6205 case scUnknown: 6206 return false; 6207 case scCouldNotCompute: 6208 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6209 return false; 6210 default: break; 6211 } 6212 llvm_unreachable("Unknown SCEV kind!"); 6213 return false; 6214} 6215 6216void ScalarEvolution::forgetMemoizedResults(const SCEV *S) { 6217 ValuesAtScopes.erase(S); 6218 LoopDispositions.erase(S); 6219 BlockDispositions.erase(S); 6220 UnsignedRanges.erase(S); 6221 SignedRanges.erase(S); 6222} 6223